Hearing the claims in the presence of the other side:
It is forbidden for a judge to hear the claims of one side of the case not in the presence of the other side. This prohibition applies equally for the plaintiff/defendant, that they may not make a claim in front of the judge unless the other person is present. [The Zohar states that one who hears one side without the other is considered as if he has accepted upon himself a foreign G-d.]
If one does not plan on judging the case: If one does not plan on judging the case, then it is permitted for him to hear one side not in the presence of the other. This applies even if there is a possibility that he may judge the case, but he does not know for certain that he will do so, he may nevertheless hear the claims of one not in front of the other, and then if he is asked to judge the case, he may do so with the consent of the other side, [after letting them know that he already heard the other side]. If however one does plan on being the judge in the case, then he may not initially hear the testimony.
If the other side consents, may the judge hear the claim not in the other’s presence?
If the both sides consent that the judge hear the claim of one side without the other then it seemingly is permitted to do so.
 Michaber 17/5; Rebbe Chanina in Sanhedrin 7b;
 Biblical or Rabbinical: Some Poskim rule it is a Biblical prohibition for the judge to hear one side without the other. [Kneses Hagedola 17/13, brought in Pischeiy Teshuvah 17/8] See Pischeiy Teshuvah ibid
 The reason: The verse states “Ushimoa Bein Acheichem Ushifatitem”, which means that the judges must hear the claims of one side in front of the other side. [Smeh 17/10; Sanhedrin ibid] Alternatively, the reason is because the verse states “Lo Sisa Sheima Shav”, and when one side makes a claim out of the presence of the other, he has no shame to make dubious claims and statements. [Smeh ibid; Beir Hagoleh ibid; Rav Kahana in Sanhedrin ibid] This then leads to fear that the fictitious claims that were aleady heard were absorbed in the mind of the judge as true. [Smeh 17/11; Aruch Hashulchan 17/7]
 The reason: As the verse states “Lo Sisa Sheima Shav” and can be read as “Lo Sasi.” [Smeh 17/12; Sanhedrin ibid]
 Zohar Vayeishev p. 149, brought in Pischeiy Teshuvah ibid; Aruch Hashuclhan 17/7
 Shach 17/9; Implication of Smeh 17/11; Poskim brought in Kneses Hagedola 17/13 and Pischeiy Teshuvah 17/8; Vetzaruch Iyun from Rama ibid who implies that even Bedieved one may only hear the case if the defendant agrees.
 Kneses Hagedola ibid
 Rama 17/5; Smeh 17/11
 The reason: As perhaps the other side does not feel comfortable being judged by a person who already heard the claim against him. [Smeh ibid]
 Clear implication of Ram and Smeh ibid; See Aruch Hashulchan ibid