How much of the pot must be insulated for it to be considered a prohibited insulation?[1]

Lechatchila, one should consider it to be prohibited insulation even if only majority of the walls of the pot are covered, even if its top is uncovered by the insulation material.[2] Thus, one is not to initially wrap the majority of the walls of a pot in a towel if the pot is on a heat source [such as a Blech, as explained in A]. However, by a pressing situation, or Bedieved, one may be lenient that as long as the pot is not fully covered by the insulation, [such as that one covered only its walls and left its top uncovered[3]], then it is not defined as insulation and is permitted to be done.[4] If only minority of the pot is covered by the insulation, then it is not defined as insulation at all even if the cover of the pot is covered with insulation, and is thus allowed to be done even Lechatchila.[5]

^[1] See Shabbos Kehalacha Vol. 2 page 14-24; Piskeiy Teshuvos 257:11

Mahadurah Basra-Ruling that majority of walls is considered insulation: Implication of Admur in Mahadurah Basra 259 [In the Mahadurah Basra for chapter 259 the Alter Rebbe elaborates on the opinions who rule that by insulation which adds heat we do not take the top of the pot into account. Thus, possibly even if only majority of the walls are covered, it would be defined as forbidden insulation. This opinion of Admur in the Mahadurah Basra is not mentioned in Ketzos Hashulchan chapter 71]; Sefer Hayashar of Rabbeinu Tam 189; Chayeh Adam 4:22; M”B 257:43 in name of Chayeh Adam ibid; Keren Ledavid 77; Toras Shabbos 253:8; Shabbos Kehalacha Vol. 2 page 14-24; Piskeiy Teshuvos 257:11; Rav Shlomo Zalman Aurbach brought in Otzros Shabbos  p. 515

Ruling of Rama and Shulchan Aruch Admur-Must be completely insulated: The definition of forbidden insulation is when the entire pot is fully covered with insulating material. [2^nd opinion and final custom in Admur 253:10; 253:14; 257:4; 257:10; Kuntrus Achron 257:3; 259 Kitzur; Rama 253:1; M”A 257:18; M”B 257:69; 258:2; Shaar Hatziyon 258:9; Ketzos Hashulchan 71 footnote 29; See Piskeiy Teshuvos 257 footnote 5 and 257:11 footnote 82; Sheivet Haleivi ; In Rishonim: Or Zarua 2:8; Ravaya 197; Mordechai 299] Background: In 253:10 and 257 10 Admur defines insulation as fully covering the entire pot with insulating material. In his words “Even if burning coals surround and are attached to the walls of the pot, [nevertheless] this is not considered [the prohibition of] insulation being that the pot is open from the top, [meaning it has no coals surrounding its top].” Similarly, in the Kuntrus Achron here number 3 the Alter Rebbe reiterates and explains this ruling, that only if both the walls and the top [meaning the pot cover] is insulated with material is it considered insulation. This ruling is also repeated here in 257:4 and in the summary of the laws of insulation brought in Chapter 259, at the very end, and is the simple understanding in chapter 253 Halacha 14. [The Sheivet Haleivi rules like this opinion, and does not make mention of the Mahadurah Basra.]

Ruling of Michaber, and opinion in Admur-Hatmana Bemiktzas: The definition of forbidden insulation is even if only a minute area of the pot is covered by the insulation material. This is called Hatmana Bemiktzas. [1^st opinion in Admur 253:10 and 257:10; Michaber 253:1; 257:8; Rabbeinu Chananel 37; Rashba 47b; Tur; Rosh; Peri Megadim 259 M”Z 3; Chazon Ish 37:19; See Shevisas Shabbos Hatmana 6] Admur ibid concludes like the former opinion

Ruling of Mishneh Berurah: It is unclear according to the Mishneh Berurah, whether he holds like the ruling of Admur in the Shulchan Aruch, that it must all be covered to be forbidden, or if he rules like the Mahadurah Basra of Admur that even insulating majority of the walls is not allowed. [Shabbos Kehalacha 2 p. 18; See M”B 257:69; 258:2; Shaar Hatziyon 258:9 which implies that the entire pot must be covered by the insulation material. However see M”B 257:43 in name of Chayeh Adam that implies if more than half of the walls are covered it is forbidden.]

^[2] This is based on the Mahadurah Basra [and other Poskim who rule this way] where the Alter Rebbe brings up the possibility that this is the definition of insulation, and thus we rule Lechatchila to be stringent like this opinion.

[3] By the insulation, however it may have its pot cover on it.

^[4] This is based on the ruling of Admur in his Shulchan Aruch and that of the other Poskim ibid who rule that it is not defined as insulation unless it is completely wrapped in it.

^[5] As rules Admur 253:10; 253:14; 257:4; 257:10 that the main opinion is like the Rama ibid, unlike the Michaber ibid, that Hatmana Bemiktzas is not Hatmana

Regarding if one may initially insulate the pot in a way that the entire bottom area of the walls is visibly uncovered: Rav Shlomo Zalman Aurbach permits this form of insulation, even if majority of the pot is covered by its upper side. However, Rav Farkash doubts whether one may initially rely on this ruling being that it has not been brought in any of the previous Poskim.

^[6] Shabbos Kehalacha Vol. 2 page 18; Piskeiy Teshuvos 257 footnote 5 and footnote 83

Other opinions: Some Poskim rule that we follow the food and not the pot. [Igros Moshe 4:74-4]

[7] See Ketzos Hashulchan who only records the stringency regarding Hatmana on Shabbos

[8] See Piskeiy Teshuvos 257 footnote 89