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Undershirt Tzitzis/Kapata/Robes-A four cornered garment with partially closed sides: 
Those garments that are closed by their upper half and contain a split by their lower half which forms four corners, such as occurs to those garments which are split in the front and back of their lower half, then whether these corners are obligated in Tzitzis is dependent on the length of the split. In all cases that the garment is split enough to require Tzitzis, then one must either a) tie Tzitzis to the corners or b) make it exempt from Tzitzis by rounding a corner or c) sew the sides to the point they are not split enough to require Tzitzis. If the garment contains Tzitzis but is not split enough to be obligated in Tzitzis [such as an invalid undershirt Tallis Katan], it is forbidden to recite a blessing over it, and one does not fulfill the Mitzvah of Tzitzis by wearing it.
This law is relevant to the following list of garments:
- Undershirt Tzitzis
- Pair of Tzitzis that had its sides sewed closed
- Long coats with a back split [i.e. Trench coats]
- Robes with a back split
- Split T-shirts
Majority split-Minority closed: If majority of the length of the garment [in both sides] is open, having only minority of the length closed, then it is obligated to have Tzitzis placed on its corners. Due to the prohibition of Maaras Ayin, by a minority closed Tallis Katan [i.e. undershirt Tzitzis] one must beware that the length is open to the point that it appears majority open also to an onlooker.
Majority closed-minority split: If majority of the length of the garment is closed [on even one side], having only minority of the length split, then it is not obligated to have Tzitzis placed on its corners. Nevertheless, due to the prohibition of Maaras Ayin, if it appears majority split to the onlooker, it is obligated in Tzitzis. Thus when wearing a minority split garment without Tzitzis one must beware that the length is closed to the point that it also appears majority closed to an onlooker. When wearing a minority split undershirt one must verify that the area which reaches below the belt/shirt is closed, as otherwise an onlooker who sees his undershirt protruding from under his shirt will think the entire shirt is split.
Equal length of closed and split: If the length of the garment is exactly half closed and half split, it is questionable as to whether it is obligated in Tzitzis, and one is therefore to be stringent regarding it in all matters. One is thus to a) place Tzitzis on its corners; b) not recite a blessing upon wearing it; c) not wear it on Shabbos in an area that does not have an Eruv.
Closing up the sides of a split: Those garments that contain a majority length split, of which one desires to exempt from Tzitzis, may be sewed closed in a way that majority of the length is now closed. One is required to sew the length in a way that its majority appears closed also to an onlooker. It does not suffice to close majority of the length in an unapparent way, due to the prohibition of Maaras Ayin. The use of buttons is invalid to close the length of the split, as explained next.
Buttons: A majority split garment which is closed using buttons, is Halachicly considered split in the buttoned areas, and hence remains obligated in Tzitzis. This applies even if the sides are entirely buttoned closed, from the top until the bottom of corner. If however the sides are buttoned closed with such strength that it requires a strong action to release them, then the buttoned area is considered closed. Due to Maras Ayin, one is to beware not to place buttons on the bottom of a Tallis Katan and use it to close the area that reaches below his waist. This applies even if the Tallis Katan is very long, and covers the length of one’s body, and the buttons are being placed on the upper half of the Tallis. This applies even if the buttons are loosely closed and can be opened easily, nevertheless it is forbidden due to Maras Ayin.
Ruling of Admur in Siddur-Complete split on both sides:
Every G-d fearing and Mitzvah coveting Jew, which desires to fulfill the Mitzvah of Tzitzis the entire day according to all opinions, must beware by our Tallis Katan that it be completely open on both sides. One is not to attach the sides together even through the use of buttons, and certainly not through sewing. This applies even towards the upper half of the Tallis. It goes without saying that one should not make sleeves for the Tallis. [Accordingly, G-d fearing Jews are to avoid wearing undershirt Tzitzis.]
Tallis Katan: Every G-d fearing Jew that wants to fulfill the Mitzvah of Tzitzis at all times according to all opinions, is to always wear a Tallis Katan that’s completely open on both sides. Accordingly, such a person is not to wear an undershirt Tzitzis, even if it is closed using buttons. Nevertheless, from the letter of the law, as long as majority of the length of the Tallis is opened in a way that is apparent to onlookers, it suffices.
Other garments: All garments that contain a split in both the front and back are obligated in Tzitzis if the split is majority of the length. If the split is minority of its length, it is not obligated in Tzitzis. Nevertheless, if the garment appears majority split to an onlooker, then it may not be worn [until it is further split, or has Tzitzis attached to its corners].
How does one measure the majority length?
One is to measure from the top of the garment. Thus by an undershirt Tallis Katan, one is to measure starting from the top of the sleeves. Those that measure from the bottom of the sleeve are making a mistake. Furthermore, some Poskim rule that the hole of the sleeve is considered as if it is closed and is hence not included as part of the split area, but as part of the closed area. Thus the undershirt Tallis Katan must be majority split excluding the sleeve hole.
Must a Kapata or trench coat have Tzitzis or have one of its corners rounded?
If the Kapata is majority split at its back then one must round one of the corners to exempt it from Tzitzis.
Must a robe with a back split have Tzitzis or have one of its corners rounded?
If the robe is majority split at its back then one must round one of the corners to exempt it from Tzitzis. Most male bathrobes do not contain a majority split, however many female robes contain a majority split. Such female robes are disputed amongst Poskim as to whether it is obligated in Tzitzis when worn by men. It is hence to only be worn by men if one of its corners are rounded [and does not contain a prohibition of Beged Isha].
Tallis Katan with sleeves:
From the letter of the law, a Tallis Katan may contain sleeves so long as it is majority split. Nevertheless the Arizal spoke against making sleeves by the Tallis Katan. Some however explain that this refers only to long sleeves, while a short sleeve Tallis Katan is valid even according to the Arizal. However, according to Admur in the Siddur which requires the entire Tallis to be split from top to bottom, it cannot contain any sleeves at all.
 10/16; Michaber 10/7; Hagahos Maimanis
 This applies whether the garment was manufactured this way, or whether it was completely split and one later sewed part of the top closed, or was completely closed and one cut part of the bottom open. [See Biur Halacha 10/7 “Rubo Sasum”]
 Practically, the custom today is not to tie Tzitzis on any garment that is obligated in Tzitzis, other than a Tallis Gadol or Tallis Katan, and rather when a garment is obligated in Tzitzis, as explained in this Halacha, one is to either round one of the corners, or sew majority of the sides. [Piskeiy Teshuvos 10/8]
 10/16; Michaber 10/7; Hagahos Maimanis
Other opinions: Some Poskim rule that a Tallis that is even minority attached is not obligated in Tzitzis. [opinion of the Sefri Zuta Ki Seitzei, recorded in Beis Yosef 10; Rashba 1/434; See Aruch Hashulchan 10/16; Tzitz Eliezer 6/1] Some Rishonim also hold that a Tallis is only obligated in Tzitzis if it can be worn over one’s head and wrapped over the body. [See Maharik 148; Maharam Mintz 110; Beis Yosef in name of Maharach Or Zarua; Aruch Hashulchan 10/19-20] Although the Beis Yosef negates this opinion, and Admur in the Shulchan Aruch makes no mention of it, seemingly Admur in the Siddur suspects that one should be stringent like this opinion to not fulfill the Mitzvah of Tzitzis with such a garment.
 Vetzaruch Iyun as what Maaras Ayin there would be in such a case? What transgression is there in placing Tzitzis in a majority closed garment. Perhaps however this will cause others to wear a Tallis that is majority closed and recite a blessing, and it is thus Maras Ayin.
 10/18; Levush 10/8
 The reason: As in such a case we consider it as if the entire garment is closed, and it thus does not contain corners and is therefore exempt from Tzitzis. [Admur]
 So is implied from the wording in Admur ibid “The strong buttons help exempt it from Tzitzis if it is positioned below the belt”, hence implying if it is positioned in a way of Maras Ayin then Tzitzis are required.
 Admur ibid regarding placing the strap below the belt
 As Safek Brachos Lihakel. [ibid]
 This applies even in a Karmalis. [ibid]
The reason: As perhaps the garment is exempt from Tzitzis and the fringes are thus considered like a separate item being carried. Even in a Karmalis, which is a Rabbinical carrying jurisdiction, one may not wear it, as the rule of Safek Derabanan Lihakel only applies once the action has occurred, however to initially create a situation where one will be lenient by a Safek Derabanan is forbidden. [ibid]
 10/17; M”A 10/12
 The reason: As one is easily able to open the buttons and return the split to its majority length. It is thus not considered closed in the buttoned area. [ibid]
 10/18; M”A 10/12; Kitzur SHU”A 9/1; Derech Hachaim
Other opinions: Some Poskim rule that loose buttons are not forbidden even due to Maaras Ayin. [M”B 10/29 and Biur Halacha “Laasos Kesisuma” in name of Elya Raba; Artzos Hachaim; Kneses Hagedola; Rebbe Akiva Eiger]
 The reason: Some suggest this is because Admur suspects for the opinion that requires Shiur Ituf to a Tallis Katan, and when the Tallis is closed in any area, one cannot perform Ituf with it. Alternatively, the reason is to suspect for the opinion of the Sefri Zuta [recorded in Beis Yosef 10] which holds that a Tallis that is even minority attached is not obligated in Tzitzis. [Glosses of Rav Raskin footnote 3]
 So writes Arizal in Shaar Hatzitzis 2
 M”B 10/25
 M”B ibid and Biur Halacha “Rubo” in name of Chayeh Adam and Sefer Hachaim [of Rav Kluger]
Other Poskim: The Elya Raba [brought in Derech Hachaim and Biur Halacha ibid] rules the hole is considered open and joins the split area. The Artzos Hachaim leaves this matter in question.
 Pashut based on ruling above; Piskeiy Teshuvos 10/14
Other opinions: According to some Rishonim a Kapata is exempt from Tzitzis even if majority split, as explained in previous footnotes. Practically, the Shulchan Aruch negates their opinion.
 This follows the same dispute mentioned regarding Tachrichin; See Kaf Hachaim 18/6; 19/4; Chemed Moshe in Peri Megadim 18 A”A 3; See Piskeiy Teshuvos 10 footnote 79
 Many Poskim rule it only applies when done for purposes of resembling the opposite gender, and not when done due to the cold or heat or other reasons. See Shach 182/7; Taz 182/4; Darkei Teshuvah 182/9; Shraga Hameir 7/124 regarding when the prohibition of Beged Isha applies.
 This applies according to the ruling in Shulchan Aruch that does not exempt a Tallis based on sleeves. However there are Rishonim that rule a garment with sleeves is exempt from Tzitzis. [See Aruch Hashulchan 10/19 based on Maharam Merothenberg 287]
 Brought in Beir Heiytiv 16/1; M”B 16/4
 Shaareiy Teshuvah 16/1; Kaf Hachaim 16/5