Gemara

(Beraisa): If a boy no more than nine years old that grew two hairs, they are Shuma (not Simanim of adulthood);

If a child (the Gemara in Nidah explains that this clause discusses a girl) between nine and 12 grew two hairs, they are Shuma;

R. Yosi says, they are Simanim (if she still has them when she is 12);

If a boy above 13 grew two hairs, they are Simanim.

Yevamos 33b (Mishnah): If two brothers were Mekadesh two sisters and they (mistakenly) switched wives, they are liable for Eshes Ish, Eshes Ach, Achos Ishto, and if they were Nidos, for Nidah.

(Rav Amram): If the girls were spurting Dam Nidah when the boys finished 13 years (Bar Mitzvah), all the boys' Isurim come together. If the girls finished 12 years when they were spurting, all their Isurim come together.

96b (Mishnah): A 20-year old who did not bring two hairs is like a nine-year old.

Kesuvos 50a (Abaye): My surrogate mother told me that 13 is the age to fast (on Yom Kipur) me'Es l'Es (the entire day). For a girl it is 12.

Nidah 44b (Beraisa - R. Meir): Bi'ah with a three-year old can make Kidushin;

Chachamim say, she must be three years and one day.

Opinion #1 (R. Yanai): R. Meir says that she becomes old enough to have Bi'ah on the last day of her third year. Chachamim say that this occurs the next day;

Opinion #2 (R. Yochanan): They argue about whether or not 30 days in the last year is considered like a full year.

45b (Mishnah): If a girl above 11 (full) years vows, we check her (to see if she understands Nedarim). If a girl above 12 vows, it is valid. If she vowed during her 12th year, we check her. If a boy above 12 years vows, we check him. If a boy above 13 vows, it is valid. During his 13th year, we check him.

47b (Beraisa): The years of a boy or girl must be me'Es l'Es.

(Rav Gidal citing Rav): This refers to the years of Erchin.

(Rav Yosef): It refers to the Mishnayos in 'Yotzei Dofen' (Perek 5 of Nidah, which discusses the age for Nedarim and Bi'ah).

Rav Yosef: Rav Gidal and I agree that all of these must be full years. (We argue only about what the Beraisa refers to.)

Support: Rav Gidal said that Rav said that all the years in Yotzei Dofen are full!

48b (Beraisa - R. Yehudah): Women do not check a girl (for hairs) during the Perek.

He holds that during the Perek is like afterwards; hairs brought then are Simanim.

(Beraisa - R. Shimon): Women check her during the Perek.

He holds that during the Perek is like before the Perek, i.e. hairs are not Simanim. We check now to know that these hairs are not Simanim even after the Perek.

Rishonim

Rif (Yevamos 39b): All agree that if a boy brought two hairs and he is 13 years and a day, he is an adult. This is a Siman.

Rif and Rosh (Kesuvos 18a and 4:16): Twelve is the age for a boy to fast me'Es l'Es, and for a girl.

Rambam (Hilchos Ishus 2:1): A girl is a minor for 12 full years even if she has many hairs. A girl 12 years and a day who has two hairs below is a Na'arah.

Rambam (10): A boy is a minor for 13 full years, even if he brought many hairs. If he brought two hairs below and he is 13 years and a day, he is an adult.

Rosh (Nidah 6:3): R. Tam explains that R. Yehudah and R. Shimon argue about the last day of the 12 years (and a day). The Halachah follows R. Yehudah (hairs then are Simanim).

Question (Tosfos Nidah 44b DH Sheloshim): R. Yochanan says that R. Meir and Chachamim argue about whether 30 days in a year are like a year. Perhaps they argue about whether part of a day in the fourth year suffices, or if we need me'Es l'Es from hour to hour?

Answers #1,2 (Tosfos): R. Yochanan knew that no one requires me'Es l'Es of hours. Alternatively, if they argued about this, R. Meir should have explicitly said that he requires an extra day, but it need not be complete.

Answer #3 (Ritva Nidah 47b DH Kulan): Elsewhere, R. Meir says that 30 days are like a year. Really, Chachamim require me'Es l'Es from hour to hour.

Tosfos (Rosh Hashanah 10a DH Ben): Sometimes, one day is not like a year. Some things require me'Es l'Es, e.g. 13 years and a day for a boy. The day is needed to complete me'Es l'Es.

Divrei Chamudos (Nidah 5:5): To resolve Tosfos in Rosh Hashanah and Nidah, we must say that the second answer is primary. Chachamim always require an extra day to prevent errors, to ensure me'Es l'Es of hours no matter what time of day one was born. Chachamim agree that when we do not need me'Es l'Es, part of a year is like a full year.

Rebuttal (Shach CM 35:1): The years of a boy or girl (and other things) must be me'Es l'Es (Nidah 47b). Tosfos (47b DH Kulan) does not require me'Es l'Es of hours. Tosfos in Rosh Hashanah also refers to me'Es l'Es of days. However, one answer in Tosfos (44b) requires me'Es l'Es of hours.

Mishneh l'Melech (Hilchos Ishus 2:21): In various places we require me'Es l'Es of hours. R. Tam says that R. Yehudah and R. Shimon argue about this (Nidah 48b). Others explain differently. Yevamos 34b proves that we do not require me'Es l'Es. (All of the Isurim come immediately when the day begins.)

Rebuttal (R. Akiva Eiger): Tosfos (34a DH mi'Toch) prefers a text which says 'the boys' Isurim come at once if the girls were spurting when they turned three. The girls' Isurim come at once if they were spurting when they turned 12.' According to this, there is no proof.

Question: Rashi (Erchin 18a DH me'Es) explains that 'the years for boys and girls' are me'Es l'Es. Rashi's text in Yevamos implies that a child becomes Bar or Bas Mitzvah at the start of the day!

Answer (Avi Ezri Ishus 2:21): 'The years for boys and girls' refers to Nedarim. The Rambam (Hilchos Nedarim 11:3) says that we need not check vows of a boy or girl above13 (or 12) years me'Es l'Es of hours, even without Simanim. Normally, the year extends me'Es l'Es of hours. However, part of the day is like the entire day if he brought Simanim. This is the case in Yevamos.

Poskim

Rema (OC 53:10): A minor should not be Shali'ach Tzibur even for Ma'ariv. Even if he reaches 13 years on Shabbos, he should not be Shali'ach Tzibur for Ma'ariv(of Shabbos) because he is not yet 13 (Maharil).

Bach (Sof ha'Siman DH Kosav Maharil): This is because we pray Ma'ariv before night. The boy may be Shali'ach Tzibur after nightfall. We require only 13 full years, i.e. but not hours before. No extra day is needed. I proved in a Teshuvah (Yeshanos 145) that he is 13 once night begins. (No one said that the Tana'im argue about whether we require me'Es l'Es from hour to hour on the first day of the next year, for it was known that no one requires this.)

Mahari Berona (cited in Sha'arei Teshuvah 13): We require me'Es l'Es on the day that begins the 14th year. The extra day is mentioned throughout Yotzei Dofen, and the Rif and Rosh (Nidah 6:2) require it.

Note: The text of the Rosh of the Mishneh l'Melech (Ishus 4:7 DH Shuv) does not mention the extra day. In our text of the Rosh, 'and a day' is in brackets.

Shulchan Aruch (55:9): One is a minor until he brings two hairs after 13 years and one day.

Mishnah Berurah (42): Even one moment of the extra day suffices. If one was born on Rosh Hashanah, even at the end of the day (but surely before night), he becomes Bar Mitzvah on the night of Rosh Hashanah of the 14th year.

Rema (616:2): Even if a 13 year old boy or 12 year old girl is weak, he (or she) must complete the fast of Yom Kipur. Perhaps he brought hairs, and they fell out.

Milchamos Hash-m (Yoma 4a): In Yotzei Dofen it says 13 years and a day, for adulthood is not until the 13 years are completed. Regarding fasting on Yom Kipur it omits 'and a day' to teach that one who turns 13 on Yom Kipur must complete the fast mid'Oraisa, for the day and adulthood come together.

Chasam Sofer (OC 172 DH Tinok): The Ra'avad (in Shitah Kesuvos 50a) says that Abaye's mother teaches that one who was 13 'me'Es l'Es' on Yom Kipur must fast. The Rashba says that the Chidush is that he must fast me'Es l'Es. It seems that me'Es l'Es applies to both. One who turns 13 that day is liable in other Mitzvos; the Chazakah is that hairs came soon after the day began. We obligate fasting from the very start of Yom Kipur, lest he brought hairs immediately. He is liable for eating then if indeed he brought two hairs.

Mishnah Berurah (12): This refers to one who turned 13 before Yom Kipur, or even on Yom Kipur but he was not checked continuously throughout the day.

Yom Teru'ah (Rosh Hashanah 28 DH Sholchu): Those who require me'Es l'Es for adulthood hold that if one was born on Rosh Hashanah at noon and heard the Shofar in the morning, he must hear it again after noon.

R. Akiva Eiger: If he brought hairs after noon, all require him to hear it again.