Gemara

(Mishnah): One's Rebbi's Aveidah takes precedence over his father's. This is because his father brought him to this world, but his Rebbi, who taught him Chachmah, brings him to eternal life;

(Beraisa - R. Meir): This refers to the Rebbi who taught him to Chachmah (the reasons for the Mishnayos and how to resolve difficulties), not the Rebbi who taught to him Mikra (written Torah) or the text of the Mishnayos;

R. Yehudah says, it is whom he learned most of his Chachmah from;

R. Yosi says, even if he explained only one Mishnah to him, he is considered his Rebbi.

(R. Yochanan): The Halachah follows R. Yehudah.

(Rav Acha bar Rav Huna): The Halachah follows R. Yosi.

Question: Did R. Yochanan really rule like R. Yehudah? R. Yochanan taught that the Halachah follows a Stam (anonymous) Mishnah!

(Mishnah): ...His Rebbi who taught to him Chachmah... (this is like R. Meir)!

Answer: It means 'who taught to him most of his Chachmah.' It is like R. Yehudah.

Mo'ed Katan 25a (Beraisa): When a Chacham dies, everyone is like a relative. One must tear, bare (his shoulder) and eat the first meal after the burial from others' food in the street.

When Rav Safra died, Rabanan did not tear for him, because they had not learned from him.

Abaye: The Beraisa does not say that we tear (only) for a Rebbi. We tear for a Chacham who died! Also, every day we recite Rav Safra's teachings!

Rishonim

Rif: Ula taught that Chachamim in Bavel rise for each other and tear clothing over each other. For an Aveidah, they give precedence only to their Ravo Muvhak (primary Rebbi) over their fathers.

Nimukei Yosef (Bava Metzia 18a DH Omar): Chachamim in Bavel were stringent. Each considered everyone else like his Ravo Muvhak. They stood for each other even outside four Amos, and would tear and never Me'acheh (sew it back straight). The Ramban disagrees. He says that they were stringent to stand (within four Amos) and to tear (but do Ichuy) even for smaller Chachamim.

Rambam (Hilchos Talmud Torah 5:9): When one's Rebbi dies, he tears all his garments until he bares his heart. He may never be Me'acheh. This refers to Ravo Muvhak who taught to him most of his Chachmah. If not, he is a Talmid Chaver, and tears for him like for other Mesim for which one is Mis'avel. This is even if he learned from him only one thing.

Kesef Mishneh (6:12): For a regular person, the Gadol ha'Dor is like his Rebbi.

Rambam (Hilchos Evel 9:2): One tears for the Rebbi who taught to him Chachmah (or the Nasi or Av Beis Din) the way he tears for a parent.

Radvaz: This is like R. Yochanan, who rules like R. Yehudah. The Rambam did not discuss a Rebbi who did not teach most of his Chachmah. He relies on what he wrote in Hilchos Talmud Torah

Hagahos Maimoniyos (1): Avi ha'Ezri says that we follow R. Yosi because Rav Sheshes, Rava and Ula hold like him, and they are Basra. Also, we generally rule like R. Yosi against R. Yehudah. Only R. Yochanan established the Mishnah in Bava Metzia like R. Yehudah.

Rambam (11): For a Chacham, one tears until he bears his heart.

Rambam (Hilchos Gezeilah 12:2): If one encountered the Aveidah of his Rebbi and the Aveidah of his father, if his father was equal (in Chachmah) to his Rebbi, his father's comes first. If not, his Rebbi's has precedence. This refers to Ravo Muvhak, from whom he learned most of his Chachmah.

Ra'avad (in Shitah Mekubetzes 33a): R. Yehudah holds that whoever taught him the majority of each Chachmah is his Ravo Muvhak

Ritva (in Shitah Mekubetzes 33a): R. Yosi holds that even if he explained only one Mishnah to him, he is considered his Rebbi for everything, including Aveidah.

Aruch ha'Shulchan (YD 242:19): This is like the Yerushalmi. It seems that the Rambam and Rashi agree. One can have more than one Ravo Muvhak, i..e the one who taught to him most of his Mikra, and most of his Mishnah... R. Meir learned from R. Yishmael and R. Akiva. Rav Yehudah learned from Rav and Shmuel. Abaye and Rava learned from Rabah and Rav Yosef. In every case, both of these were considered Ravo Muvhak.

Rosh (Bava Metzia 2:30): The Halachah follows R. Yochanan (who rules like R. Yehudah, that one's Rebbi is the one who taught him most of his Chachmah), for Ula agrees.

Poskim

Shulchan Aruch (YD 242:25): When one's Rebbi dies he tears all his garments, until he bares his heart...

Shulchan Aruch (30 and 340:8): These laws apply to Ravo Muvhak from whom he learned most of his Chachmah, be it Mikra, Mishnah or Gemara.

Beis Yosef (DH umi'Toch): The Tur (brought below) equated Ravo she'Eino Muvhak and Talmidim in Bavel (for each other). This is like the Rambam and Ramban. Regarding tearing, he says that one is not Me'acheh even for one who taught to him one Halachah! He did not specify that this is for Chachamim in Bavel! Indeed, R. Chananel and Avi ha'Ezri say so, but they rule like R. Yosi!

Lechem Mishneh (Hilchos Evel 9:11): The Rambam says that one bears his heart for a Chacham. The Tur says that this is even for Ravo she'Eino Muvhak. This is difficult, for the Rambam explicitly rules like R. Yehudah, that Ravo Muvhak is only one who taught to him most of his Chachmah! The Tur understood like Rashi, that even R. Yehudah agrees that one is not Me'acheh even for Ravo she'Eino Muvhak. The Beis Yosef assumed that the Tur holds like Maharik, Ran and Nimukei Yosef, that this is only for Ravo Muvhak, therefore, he asked his question. The Rosh (Mo'ed Katan 3:42) explicitly says like I explained the Tur.

Rema: Nowadays, Ravo Muvhak is not the one who taught him Pilpul and distinctions, rather, one who taught Pesak Halachah, investigation and guided him to what is true and straight.

Maharik (169:2): R. Achai Gaon, the Rambam, R. Yeshayah, the Rosh and Tur all rule like R. Yehudah. Ravo Muvhak pertains to ruling in front of one's Rebbi, harboring ill thoughts about him or conflicting with him. If he did not learn from him most of his Chachmah, he is like a Talmid Chaver, and just stands and tears for him. We learn all of these from Moshe Rabbeinu. Nadav and Avihu died for ruling in front of him, Dasan and Aviram died for making a controversy with him, and Bnei Yisrael were rebuked for speaking 'against Hash-m and against Moshe.' All these apply to one like Moshe, i.e. Ravo Muvhak. R. Chananel and Avi ha'Ezri rule like R. Yosi. It seems that R. Yosi did not mean that one who explained one Mishnah is like Ravo Muvhak for all these laws, just for tearing for him and standing for him even if the Talmid became a great Chacham. The Mordechai rules like R. Yosi because Rav Sheshes, Rava and Ula hold like him. Regarding Aveidah, Ula holds like R. Yehudah! This shows that R. Yosi agrees that one who explained one Mishnah is not Ravo Muvhak for Aveidah (and other laws). Tearing is different; we learn from "Avi Avi Rechev Yisrael..." that one tears even for Ravo she'Eino Muvhak.

Shulchan Aruch (ibid.): If he did not learn most of his Chachmah from him, he tears from him like for any relative for which there is Aveilus. This is even if he learned from him one matter, be it big or small.

Rema (340:8): Some say that one is not Me'acheh even for Ravo she'Eino Muvhak. If Chachamim learn together and answer questions for each other, some say that each is like Ravo she'Eino Muvhak for each other, and some say that each is like Ravo Muvhak for each other. Some say that one must tear only for the Rebbi from whom he learned most of his Chachmah. It is a stringency for colleagues who learn together to tear for each other, or for one from whom he learned one matter. This applies only where it is the custom; we do not tell people to be stringent. This is why people are lenient in our lands.

Tur: For a Rav who only taught Chachmah, one tears and can be Me'acheh. The Ramban says that one is not Me'acheh. The Rambam says that one tears all his garments. The Rosh holds like the Rambam.