Gemara

(Rav Nachman): We check boys above 13 (and girls above 12) for hairs regarding Kidushin, divorce, Chalitzah, and Mi'un (retroactive annulment of a marriage mid'Rabanan).

Nidah 46a (Rava): A girl may do Mi'un anytime until 12 full years. After 12, she may not do Mi'un or Chalitzah.

Question: He forbids Mi'un because he assumes that she is an adult (and the marriage became mid'Oraisa). If she is an adult, she should be permitted to do Chalitzah!

Rava is not in Safek whether she is an adult, for he taught that we need not check a girl above 12. She is Muchzekes to be an adult.

Answer #1: Normally, we assume that she is an adult. She may not do Chalitzah in a case when we see that she does not have hairs now. She may not do Mi'un, lest she brought hairs after 12 years, and they fell out.

Question: This is according to the opinion that is concerned that they fell out. According to the opinion that is not concerned, how can we answer?

Answer #2: We did not check her. Regarding Chalitzah we are concerned (lest she is still a minor). Rava's Chazakah refers to Mi'un (we are stringent not to allow Mi'un). She may not do Chalitzah until we see hairs.

(Rav Dimi of Neharde'a): The Halachah is, we are concerned that they fell out (regarding Mi'un) only if she had relations with her husband after 12 years of age, for then it is a Safek mid'Oraisa). If not, she may do Mi'un (since she is married only mid'Rabanan).

47b (Beraisa - R. Chiya): If one does not have Simanim, he is a minor until the majority of a normal lifetime (i.e. the start of his 36th year).

Berachos 47b (R. Yochanan): A minor Pore'ach joins for a Zimun.

Support (Beraisa): A boy joins for a Zimun only if he has two hairs. We are not particular about minors.

The latter clause includes a minor Pore'ach.

The Halachah is unlike all these teachings, rather, like the following:

(Rav Nachman): If a minor knows to Whom we bless, he joins for a Zimun.

Rishonim

Tosfos (Berachos 47b DH Katan): A minor Pore'ach is one who brought two hairs before 13 years. The hairs are less than the required Shi'ur. Rashi says that they are full hairs.

Rif (Berachos 35a): A minor who knows to Whom we bless joins for a Zimun. Rabanan say that this is if he is in his 13th year, even if he was not Pore'ach. Before this, even if he was Pore'ach he does not join. I hold that 'minor' includes a boy of nine or 10.

Rosh (Berachos 7:20): The first Perush is R. Chananel. The Yerushalmi requires two hairs. It seems that we do not join a minor for a Minyan of 10 for Birkas ha'Mazon, Tefilah or to three (for Birkas ha'Mazon) until he brings two hairs.

Rambam (Hilchos Tefilah 8:4): Tefilah b'Tzibur requires 10 adults.

Kesef Mishneh: The Rambam holds that the Gemara allows a minor (who knows to Whom we bless) to join only for a Zimun.

Rambam (Hilchos Ishus 2:15): If a boy above 13 did not bring a Siman below, and he brought all the Simanim above, it is a Safek whether he is a minor of adult. If he was not checked below, since he has Simanei Bagrus above, he is assumed to be an adult.

Poskim

Shulchan Aruch (OC 55:5): If one did not bring two hairs, even if he is old he is a child (and cannot join for a Minyan) until the majority of his years.

Mishnah Berurah (25): Two hairs in other parts of the body, e.g. the beard, also help.

Kaf ha'Chayim (43): If he has a full beard, one need not look for other hairs.

Rema: We are not particular about hairs. Whoever reached the required years, we establish him to be an adult for this, and we say that presumably he brought two hairs.

Beis Yosef (DH v'Chosav ha'Rosh): The Rashba (1:453) says that a minor does not join for Tefilah, Kaddish or Borchu until 13 years and two full hairs, or at least incomplete hairs and he knows Whom we bless. In another Teshuvah (239) he requires a true adult. Also the Rambam says so. The Ra'avad derives this from Bereishis Rabah (91:3).

Beis Yosef (DH u'Mashma): The Tur connotes that even if he is big, he does not complete a Minyan until the majority of his years, like it says in Nidah (47b).

Magen Avraham (7): The Rema is lenient for this matter, i.e. because Tefilah is mid'Rabanan.

Eshel Avraham: He means that Tefilah with a Minyan is mid'Rabanan, and "v'Nikdashti b'Soch Bnei Yisrael" is only an Asmachta. We do not rely on the Chazakah for Kidushin due to the severity of Eshes Ish. Also for Chalitzah Chachamim were stringent, for if a Yevamah marries a stranger, the child is a Mamzer. In monetary matters we do not follow the majority. However, the Poskim say that we must check for every Torah law; we do not rely on Rava's Chazakah, which is based on a majority (most bring hairs right away). What is the reason? We rely on the majority and Chazakah, even a Chazakah mid'Rabanan, for Torah laws! There are two reasons. One is that we are concerned for a common minority; this is why we must check the lungs in a slaughtered animal. The other reason is that when it is easy to verify, we do not rely on the majority or Chazakah. We need not check for all 18 Tereifos, for it is an exertion to check for a tiny hole in all of them. We would not rely on a Chazakah about Bedikas Chametz if we could ask the owner (Pesachim 4a). Toras ha'Shelamim says that for a Sefek Sefekah with a Chazakah, one need not verify, even if one could do so easily. Pesachim 4a proves otherwise, for a Safek mid'Rabanan is like a Sefek Sefekah about a Torah law. Why are we lenient about Tefilah? It is easy to check! If we will say that Chachamim were stringent about it (Bedikas Chametz) for it is a common minority, and it is hard to check for hairs, this explains why we are lenient about Tefilah mid'Rabanan.

Gra (8,14): The Yerushalmi and Bereishis Rabah say that we are not exacting about a minor. Matanos Kehunah says in the name of Rashi that if he is 13 years old, we are not exacting if he has hairs. Even though the Bavli disagrees (and says that we are not exacting about the size of the hairs), the custom is like the Yerushalmi.

Rema (199:10): Some say that we do not join a minor to a Zimun at all until he is 13 years old, and then the Chazakah is that he brought two hairs. This is our custom. One should not deviate.

Beis Yosef (DH u'Mah she'Chosav v'Adoni): The Tur, Hagahos Maimoniyos (5:6) and Semag say that a minor joins for a Zimun only after he brings two hairs. This connotes proper hairs after 13 years. This is unlike the conclusion, which is like Rav Nachman! Even though an action was done differently in the Yerushalmi, this does not override the Bavli! They must hold that even though Rav Nachman says that a minor who knows to Whom we bless joins for a Zimun, he must have brought two hairs. This is because before this we supported R. Yochanan from a Beraisa. Even though we said 'the Halachah is unlike all these teachings', they hold that even if this includes R. Yochanan's teaching, Rav Nachman does not argue with the Beraisa. Rather, we must say that Rav Nachman explains that the Beraisa allows a minor to join for a Zimun only if he knows to Whom we bless. Normally, two hairs before 13 years are not a Siman. For a Zimun, they suffice. R. Yochanan held that the hairs need not be the proper Shi'ur. He was rejected; proper hairs are required. It seems that R. Yonah agrees. He says that a minor joins for a Zimun only after he brings two hairs, or after 13 years. They and the Rosh hold that the Yerushalmi is like the Bavli's conclusion. However, the Maharik (49) requires 13 years, and says that this is like the Rosh, Tur, Ri and Semag. He understands that they require proper hairs after 13 years. If so, why did they reject the Bavli? Therefore, the first explanation is better. Since the Rif and Rambam agree, we follow them. Even though we do not join a minor to 10, that is because it is a Davar shebi'Kedushah.

Magen Avraham (7): If we know that he did not bring two hairs, we may not join him. We may not rely on the Chazakah to be Yotzei Birkas ha'Mazon through him, for this is mid'Oraisa. The Yam Shel Shlomo is lenient, for he says that mid'Oraisa one can be Yotzei through a minor. Many Gemaros and oppose this. The Ramban explicitly disagrees. Also, one can be Yotzei another due to Arvus (guarantorship), which applies only to adults.