Gemara

(Mishnah): If a girl converted below the age of three, (when she marries) her Kesuvah is 200. There is Ta'anas Besulim.

(Gemara - Rav Huna): If a minor wants to convert, we immerse him (in a Mikveh to convert him) on the volition of Beis Din.

Question: Does Rav Huna teach that Zachin l'Adam she'Lo b'Fanav (we may do something beneficial for a person in his absence)? A Mishnah teaches this!

(Mishnah): Zachin l'Adam she'Lo b'Fanav, but we cannot do Chov (something detrimental) to a person in his absence.

Answer: We might have thought that conversion is not Zechus for a Nochri, for he prefers immorality. We hold that a slave prefers immorality!

Rav Huna teaches that this applies only to an adult, who has tasted Isur. A child has not, so conversion is Zechus for him.

Support (Mishnah): If a girl converted below the age of three...

Suggestion: She was converted on the volition of Beis Din!

Rejection: No, she converted with her father. Children are happy with what their father does.

(Rav Yosef): When a child convert grows up, he can renounce the conversion.

Question (Abaye - Mishnah): If a girl converted before three, her Kesuvah is 200.

If she can renounce the conversion, would we give to her a Kesuvah?! She might return to being a Nochris and keep the money!

Answer: We do not give to her the Kesuvah until she grows up.

Question: Still, she may renounce the conversion after she receives the Kesuvah!

Answer: If she does not renounce it the moment she matures, she cannot renounce it later.

Question (Rava - Mishnah): If a man rapes a girl who converted before three, he pays her a fine. (We would not give her if she could renounce the conversion!)

Answer: We do not give to her the fine until she grows up.

Abaye did not ask Rava's question, for (even though she may renounce) we fine a rapist to punish him for his sin. Rava did not ask Abaye's question, for in any case she has a Kesuvah, lest it be light in her husband's eyes to divorce her.

Rishonim

Rif and Rosh (Yevamos 16b and Kesuvos 1:23): We immerse a minor to convert him on the volition of Beis Din. This is Zechus for him, and Zachin l'Adam she'Lo b'Fanav. We say that a Nochri prefers immorality. That applies only to an adult, who has tasted Isur. A child has not, so conversion is Zechus for him.

Rosh (ibid.): When a child convert grows up, he can renounce the conversion before we see him observe Torah and Mitzvos. From the day he matured and we saw him acting like a Yisrael, he cannot renounce the conversion. I do not know why the Rif omitted this.

Rambam (Hilchos Isurei Bi'ah 13:7): We immerse a minor to convert him on the volition of Beis Din, for this is Zechus for him.

Rambam (15:26): If a deserted baby was found in a city with Nochrim, he is a Safek Nochri. If Beis Din immersed him for conversion, he is like a deserted baby found in a city of Yisraelim.

Rambam (Hilchos Melachim 8:8): If an Eshes Yefas To'ar became pregnant from the first Bi'ah, the child is a convert. (If the mother did not convert before he was born,) Beis Din immerses him on their Da'as.

Rambam (10:3): If a Ben Noach converted, circumcised and immersed and wanted to go away from Hash-m and be just a Ger Toshav like before, we do not consent. He is a full Yisrael, or he is killed. If he was a minor when Beis Din immersed him he can protest when he grows up and be just a Ger Toshav. Since he did not protest at the time, he cannot protest later. He is a full convert.

Ran (Kesuvos 4a DH Garsinan): We immerse a minor to convert him on the volition of Beis Din. This is if he has no father and his mother brings him to convert, we immerse him. There is no conversion without circumcision and Tevilah. It is on the volition of Beis Din, i.e. there are three at his Tevilah, like every conversion. They become like his father. He is a convert through them. If he touches wine it is Kosher. When he matures he can protest, i.e. even if he converted with his father. The Gemara proves so. If he wants to return to his unruly ways Beis Din does not punish him, even if Yisrael has the upper hand. If he was Mekadesh a woman after he protested she does not need a Get, for he is not like a Yisrael Mumar. If a convert did not protest immediately (upon maturing), he or she cannot protest later.

Question: The Gemara said 'if she protested when she grew up', implying that she cannot protest before this. How can she protest precisely at the moment she matures?

Answer (Ran ibid. and DH ul'Inyan): Granted, a protest before maturity is not binding and she can retract from it. However, it suffices for her to protest before maturity and to persist with it after maturing. Alternatively, 'if she did not protest immediately after maturing, she cannot protest later' applies only if she matured amidst Torah law. The Halachah follows Rav Huna who says that we immerse a minor on the volition of Beis Din. This is not a Mitzvah for Beis Din to circumcise Nochri children. Rather, if he came or his mother brought him or Beis Din happened to do so themselves, it takes effect.

Rebuttal (Bach YD 268 DH Kosav): If a minor Nochri came to convert, even though he has no Da'as we heed him, for Zachin l'Adam she'Lo b'Fanav. If he does not want he is not a convert, even if Yisraelim have the upper hand. What is the Ran's source to say that if Beis Din converted him by themselves that it works?

Ran (ibid.): The Halachah follows Rav Yosef, who says that the child can protest, even if he converted with his father. Abaye and Rava did not challenge Rav Yosef because they disagree with him, rather, to clarify the Halachah and show that these are not difficulties. Abaye's question is not even a question according to Rava, and Rava's question is not even a question according to Abaye.

Question (Rosh, ibid. and Ran): Why did the Rif omit Rav Yosef's law?

Answer (Ran citing Ramban): The Rif holds that Rav Yosef discusses children who converted with their father. One converted by Beis Din cannot retract, for if so Beis Din would be weak. This is not clear.

Tosfos (44a DH ha'Giyores): It says 'a convert who converted with her daughter', as opposed to 'the daughter converted', because we discuss a girl below three. We do not convert a Nochri unless he wants; a child below three has no Da'as.

Tosfos (Nazir 23b DH Bas): It seems that Rus converted when she was a minor. (Converts are punished for delaying conversion. It says about Rus "Your reward will be complete.")

Poskim

Shulchan Aruch (YD 268:7): If a minor Nochri has a father, his father can convert him. If he has no father and he came to convert or his mother brought him to convert Beis Din converts him, for this is Zechus for him and Zachin l'Adam she'Lo b'Fanav.

Question (Tur and Shiltei ha'Giborim Yevamos 16b 2): BaHaG says that we do not accept a Cheresh, lunatic or child who comes to convert because he has no Da'as (understanding) to stipulate with him. However, we can circumcise a child through (the Da'as of) his fathers. I do not know why BaHaG rules unlike Rav Huna.

Answer (Beis Yosef DH Kosav): BaHaG explains that Rav Huna discusses a mother who brings her child to convert. He says that we can circumcise a child through Avosav, i.e. either parent, so we will not say that only his father can convert him.

Bach (DH Goy): The Tur connotes that his mother need not bring him. Rashi mentioned this to teach that even if his mother brings him we need Da'as Beis Din. Only when his father brings him we do not need Da'as Beis Din.

Chasam Sofer (YD 253 DH va'A'an): BaHaG rules that Beis Din does not convert a minor unless one of his parents brings him, and in this case he cannot retract. This is why the Rif did not mention that he can retract. Also the Rambam does not mention retracting in Hilchos Ishus, only in Hilchos Melachim where he discusses one who was converted Al Da'as Beis Din.

Shulchan Aruch (ibid.): Whether a minor was converted by his father or by Beis Din, when he matures he can protest.

Gra (21): We learn from Abaye's question (why do we give her a Kesuvah if she can protest? If in some case she cannot protest, this is not a question!)

Shulchan Aruch (ibid.): He is not like a Yisrael Mumar, rather, like a Nochri.

Taz (14): He is like a Nochri, i.e. his Kidushin is void.

Shulchan Aruch (8): This is if he did not act like a Yisrael after maturing. If he did, he can no longer renounce the conversion.