Gemara

16b - Beraisa - R. Yehudah: The Mizbe'ach was in the middle of the Azarah (from north to south). It was 32 Amos long; 10 Amos were opposite the opening of the Heichal, and 11 Amos on each side were opposite the walls of the Heichal.

This is unlike the Stam Tana of Midos:

Mishnah: The Azarah was 135 Amos from north to south. The ramp and Mizbe'ach together were 62; there were eight Amos from the Mizbe'ach until the rings, the rings occupied 24, from the rings to the tables was four, from the tables to the pillars was four, from the pillars to the wall of the Azarah was eight, the remainder was split between the extent of the pillars and the space from the south wall to the ramp.

Conclusion: The Stam Tana of Midos is not R. Yehudah, who says that the Mizbe'ach was in the middle. Rather, it is R. Eliezer ben Yakov (who says that it was in the south).

37a - Mishnah: The Kohen Gadol came to the east part of the Azarah, north of the Mizbe'ach...

Inference: It did not suffice to be east of (and even with) the Mizbe'ach. He needed to be north of the Mizbe'ach, for the Mizbe'ach itself is not in the north. The Mishnah is like R. Eliezer ben Yakov:

Beraisa - R. Eliezer ben Yakov: "Tzafonah" - the north must be totally empty (even the Mizbe'ach may not be there).

Question: The previous Mishnah (34b) considers between the Mizbe'ach and the Ulam to be Tzafon (which is Kosher for Shechitas Kodshei Kodoshim), like R. Elazar b'Rebbi Shimon (i.e. the Mizbe'ach itself is in Tzafon)!

Answer: Also that Mishnah is like R. Eliezer ben Yakov. It considers what is next to between the Mizbe'ach and the Ulam (but further north) to be Tzafon.

Rishonim

Question: R. Eliezer ben Yakov expounds that the Mizbe'ach cannot be even partially in the north. If so, the ramp must begin within five and a half Amos of the southern wall. (The entire Mizbe'ach is 62, and the southern half of the Azarah is 67 and a half Amos.) If half of the remaining 25 Amos (or 21, if we allow four Amos for the tables) are between the Mizbe'ach and the south wall, this is too much!

Answer #1 (Rashi 17a DH Ela): The remaining Amos are not divided equally. Rather, only five and a half are between the Mizbe'ach and the south wall.

Question: If we need not divide the remaining Amos equally, the Mishnah could be like R. Yehudah! If 21 and a half Amos are between the Mizbe'ach and the south wall, the Mizbe'ach is in the middle!

Answer (Rashi, ibid.): This would leave only three and a half Amos for the pillars and tables; this is unreasonable.

Objection (Rashi 16b Sof DH Ruva): If the remaining Amos are not divided equally, the Tana should have taught how they are divided!

Answer #2 (Rashi 17a DH Ela.): They are divided equally. The correct text does not conclude that the Stam Tana of Midos is R. Eliezer ben Yakov. Rather, it only says that it is not R. Yehudah.

Rambam (Hilchos Beis ha'Bechirah 5:13-15): The Azarah was 135 Amos from north to south. There were eight Amos from the north wall to Beis ha'Mitbechayim. Beis ha'Mitbechayim was 12 and a half Amos, In the next eight Amos were eight marble tables on which sections of animals were placed and meat was washed before cooking. The rings occupied 24 Amos; there were eight Amos between the rings and the Mizbe'ach. The Mizbe'ach was 32 Amos and the ramp was 30; there were 12 and a half Amos between the Mizbe'ach and the south wall. There were 60 and a half Amos between the Mizbe'ach and the north wall.

Rambam (Hilchos Avodas Yom Kipur 3:2): The lottery is done in the east part of the Azarah, north of the Mizbe'ach.

Rambam (ibid. 4:1): ...The Kohen Gadol's bull stands between the Ulam and the Mizbe'ach...he slaughters it...

Question (Kesef Mishneh 3:2): In Halachah 3:2 the Rambam rules like R. Eliezer ben Yakov, and in 4:1 he rules like R. Elazar b'Rebbi Shimon. The Gemara (37a) asked this contradiction in the Mishnayos, and was forced to change the text to say next to between the Mizbe'ach and the Ulam!

Answer #1 (Kesef Mishneh): We must similarly correct the text of the Rambam. The Rambam rules like R. Eliezer ben Yakov because he is the Stam Tana of Midos. Also, the Halachah always follows R. Eliezer ben Yakov.

Rebuttal (and Answer #2 - Tosfos Yom Tov Yoma 3:9): This cannot be, because of Rashi's question! The Rambam explains that the Mizbe'ach ended 74 and a half Amos from the south wall, i.e. the last seven Amos were in the north! Even though Perush ha'Mishnayos (Midos 2:5) says that the Stam Tana of Midos is R. Eliezer ben Yakov, there are exceptions. The Rambam rules like a different Stam Mishnah at the end of Midos, which is like Rebbi.

Answer #3 (Chazon Ish Nega'im 12:7): The Rambam's text was like Rashi's. On 17a it does not conclude that the Tana is R. Eliezer ben Yakov. Even though some Mishnayos in Midos are unlike R. Eliezer ben Yakov, we establish as much as possible like him. It is possible that the Beraisa in which R. Eliezer ben Yakov says that Tzafon is empty holds that the Mizbe'ach is there. Since it is Kadosh it is not an interruption.

Note Tosfos (Zevachim 59a DH Panuy) says that Tzafon need not be clear of tables, rings or pillars, which are needed for Shechitah.

Chazon Ish (Likutei Zevachim p.149:7): Alternatively, the Beraisa argues with the Mishnah in Midos about the opinion of R. Eliezer ben Yakov.

Rambam (Hilchos Temidim u'Musafim 2:8): The second Ma'arachah, for Ketores, was five Amos north of the southwest corner.

Question: Zevachim 58 established this like the opinion that the entire Mizbe'ach is in the north, for then five Amos from the south of the Mizbe'ach is opposite Pesach ha'Heichal. But according to R. Yehudah, the Mizbe'ach is in the middle of the Azarah, so the Ma'arachah must be at least six Amos from the south to be opposite the Pesach. The Rambam holds that most of the Mizbe'ach is in the south. If so, the Ma'arachah must be even more towards the north of the Mizbe'ach to be opposite the Pesach!

Answer (Lechem Mishneh): The Rambam holds that that Gemara is according to R. Yosi, but the other Tana'im do not require the Ma'arachah to be opposite the Pesach.