Gemara

5b: Once, a Chacham expounded, and people midunderstood him. It was decreed that a Talmid needs Reshus (permission) to teach Halachos.

Tanchum brei d'R. Ami came to a place. He permitted to wet wheat (on Pesach) just before grinding it. They told him that his Rebbi was there.

(Beraisa): A Talmid may not teach Halachos within three Parsa'os of his Rebbi, corresponding to the length of Machaneh Yisrael.

Tanchum: I was unaware.

36a (Rav Ada bar Ahavah): From the time of Rebbi until Rav Ashi, the greatest Chacham was never the leader.

(Rav): In capital cases, one may explain the reasons for Zechus and Chiyuv to his Talmid, and the Talmid is also counted in the vote on the verdict.

36b: Rav referred to Talmidim such as Rav Kahana and Rav Asi, who needed to hear teachings from a Rebbi, but could reason by themselves, and did not need a Rebbi for this.

Eruvin 62b: Rav Chisda ruled in Kafri while Rav Huna was alive.

(It was enacted that a slaughterer must bring his knife to the local Chacham to inspect it, for the honor of the Chacham.) Ravina inspected a knife in Bavel. His Rebbi, Rav Ashi, asked why he did so.

Ravina: (You were in a different city. Also) Rav Hamnuna gave rulings in Charta while Rav Chisda was alive (elsewhere)!

Rav Ashi: It was taught that Rav Hamnuna did not give rulings!

Ravina: He did not rule in the life of his Rebbi, Rav Huna, but he did in Rav Chisda's life, for he was a Talmid Chaver. I am a Talmid Chaver to you!

Rishonim

Rambam (Hilchos Talmud Torah 5:9): Rabo Muvhak is the Rebbi who taught to him most of his Chachmah. If he did not learn most from him, he is a Talmid Chaver.

Hagahos Maimoniyos (40): A Talmid Chaver may rule outside of three Parsa'os. Rashi explains that Rav Chisda ruled in Kafri while Rav Huna was in Pumbadisa. Rav Hamnuna ruled in Charta while Rav Chisda was alive, for he was a Talmid Chaver. This is with Reshus, like the case of R. Tanchum.

Rosh (Eruvin 6:2): Presumably, the Heter for a Talmid Chaver is only outside of three Parsa'os.

Poskim

Shulchan Aruch (YD 242:4): If one was three Parsa'os from his Rebbi and someone happened to ask a Halachah, he may answer. He may not fix himself to rule for all who ask, even if he and his Rebbi are at opposite ends of the world, until his Rebbi dies or gives Reshus.

Gra (8): The Rashba (111) says that Sanhedrin 5b discusses a Stam Talmid, i.e. even a proper Talmid. Letter of the law, outside of three Parsa'os is permitted. 'In front of him' is right in front of, and 'not in front' is within three Parsa'os. We decree to forbid even outside of three Parsa'os. Within three Parsa'os, letter of the law it is forbidden, so Reshus does not help. He must say that Rav Hamnuna did not rule because he was within three Parsa'os of Rav Huna, but he ruled within three Parsa'os of Rav Chisda, i.e. for this is permitted to a Talmid Chaver.

Rema: This refers to one's primary Rebbi. A Talmid Chaver is permitted even within three Parsa'os. Some say that in any case it is forbidden right in front of one's Rebbi.

Shach (6): The latter opinion forbids even a Talmid Chaver right in front of one's Rebbi.

Gra (9): The Rema said 'some say', for the Beis Yosef says that the Rambam permits. Really, all forbid (see Gra 8 citing the Rashba).

Shulchan Aruch (ibid): A Talmid Chaver is forbidden but exempt within three Parsa'os, and permitted outside of three Parsa'os.

Shach (10): The Shulchan Aruch connotes that outside of three Parsa'os is permitted even without Reshus. Rav Hamnuna did not rule in the life of Rav Huna, but he ruled in the life of Rav Chisda. This was without Reshus, and outside of three Parsa'os, for he was a Talmid Chaver. Hagahos Maimoniyos holds that he always needs Reshus.

Maharik (169): Do not say that Tosfos permits a Talmid Chaver without Reshus outside of three Parsa'os. Tosfos brought no source for this. We have no source that Rav Chisda was a Talmid Chaver of Rav Huna. Within one city is like in front of him, for Rav Chisda was fixed, like a Beis Din. The Gemara did not need to explain why Rav Hamnuna ruled in the life of Rav Chisda, but not in Rav Huna's life, for it was known that he was a Talmid Chaver of Rav Chisda and a proper Talmid of Rav Huna. If it was because he received Reshus only from Rav Chisda, the Gemara would have needed to specify!

Maharik (169): Sanhedrin 5b taught the decree that a Talmid must receive Reshus to rule even far away, lest people err about his words. Why did it bring the case of R. Tanchum, which is relevant to ruling in front of a Rebbi? Maharam concluded that general Reshus to rule does not permit within three Parsa'os of one's Rebbi, even for a Talmid Chaver. Presumably, R. Tanchum would have known where his primary Rebbi is. Alternatively, the Gemara knew that he was a Talmid Chaver.

Shach (11): A Talmid Chaver needs Reshus only from his Rebbi (i.e. one of them). If one is his primary Rebbi, he needs his Reshus.

Rema: Here, Rabo Muvhak cannot mean like its usual meaning, that he learned most of his Chachmah from him, for if so, one cannot have more than one! Rather, itm a proper Talmid, to exclude a Talmid Chaver, i.e. a Talmid who grew in Torah and became a colleague, i.e. almost as great a Chacham as his Rebbi.

Beis Yosef (DH v'Nir'eh): The Rambam connotes that a Talmid Chaver may rule even in front of his Rebbi. The Isur to rule applies only to Rabo Muvhak. It seems that the Rif (Eruvin 19a) agrees, and therefore he omitted the episode with Rav Ashi and Ravina. If he held like the Rosh, he should have brought the episode to teach that a Talmid Chaver may not rule in front of his Rebbi! The Maharik says that a Talmid Chaver is one who was originally a Talmid, and became a colleague, even if he is not as Chacham as his Rebbi, but he is close. The Rambam holds that it is only if he learned the minority of his Chachmah from him. If he learned the majority, it would not matter if now he is as great as him!

Maharik (169): One is considered a Talmid Chaver if he became close to the level of his Rebbi. He need not be as great. Ravina was a Talmid Chaver of Rav Ashi, even though Rav Ashi was greater (Sanhedrin 36a). The Ri says that the Halachah follows Rav Ashi against Ravina. If Ravina became as great, we should follow him, for he is Basra! R. Yosef Tuv Elem rules like Ravina. Perhaps this is because he was Basra, even if he was not as great. Rav Chisda was a Talmid Chaver of Rav Huna, even though he never became as great. Rava prayed to became as Chacham as Rav Huna and as wealthy as Rav Chisda (Mo'ed Katan 28a). He did not attribute both of them to one person. This was after Rav Huna died, so we cannot say that afterwards Rav Chisda became as great as Rav Huna (in Rav Huna's lifetime). If R. Chiya became as great as Rebbi, we should rule like a Stam Tosefta (of R. Chiya) when there is an argument in the Mishnah (which shows that Rebbi was undecided)!

Gra (12): The Rivash (271) learns from R. Yirmeyah bar Aba, who was a Talmid Chaver of Rav, even though Rav was greater than even R. Yochanan. This shows that the Talmid need not became as great as his Rebbi.

Rema: However, some distinguish and hold that if he received Reshus from his Rebbi, it helps to rule outside of three Parsa'os, but not within three Parsa'os. Some say that as long as he is not Rabo Muvhak, i.e. he did not learn most of his Chachmah from him, he is a Talmid Chaver.

Shach (13): The Levush holds that Reshus from all his Rebbeyim (or if he has only one) permits within three Parsa'os. Some disagree.

Gra (14): Rashi holds that Reish Lakish learned primarily from R. Yochanan. He must say that Reshus helps (even in front of him).