Gemara

A Nochri boasted 'I eat from the choicest part of the Pesach!'

R. Yehudah ben Beseira suggested that he ask for the tail. He did so. They investigated, found that he was a Nochri, and killed him.

Yevamos 45a: Rav Yehudah would counsel the son of a Yisraelis from a Nochri or slave to go to a place where he is unknown, and get married there.

45b: People were calling a certain man the son of a Nochris.

Rav Asi: Didn't his mother immerse after being a Nidah?!

People were calling a certain man the son of a Nochri.

R. Yehoshua ben Levi: Didn't his father immerse after Keri (seminal emissions)?!

47a (Beraisa - R. Yehudah) Suggestion: If a man claims to be a convert, perhaps we accept him!

Rejection: "Itcha (with you)" - we accept him only if he is Muchzak (established) to you. "Itcha" connotes whenever you are.

"B'Artzechem" teaches that in Eretz Yisrael, the convert must bring proof. In Chutz la'Aretz, he does not need proof;

Chachamim say, in every place he must bring proof.

Question: Why must a verse teach about one who has witnesses?

Answer (Rav Sheshes): The witnesses say 'we heard that he converted in Ploni's Beis Din';

The verse teaches that we believe them.

(R. Chiya bar Aba): The Halachah is, both in Eretz Yisrael and Chutz la'Aretz, he must bring a proof.

(Beraisa): A man told R. Yehudah that he converted by himself. He had no witnesses, and he had children.

R. Yehudah: You are believed to disqualify yourself, but not to disqualify your children.

Rishonim

Rambam (Hilchos Isurei Bi'ah 13:7): If one converted by himself, or even in front of two, he is not a convert. If he said 'I converted in Ploni's Beis Din and they immersed me', he is not believed to marry a Yisrael until he brings witnesses.

Rambam (10): If one comes and says that he was a Nochri and he converted in Beis Din, he is believed, for the one who forbade is believed to permit. This is in Eretz Yisrael, when everyone there was Muchzak to be a Yisrael. In Chutz la'Aretz one must bring a proof, and then he may marry a Yisraelis. I say that this is a stringency of lineage.

Rebuttal (Ra'avad): R. Yehudah requires a proof in Eretz Yisrael, but not in Chutz la'Aretz, and in all places Chachamim require a proof!

Rosh (Yevamos 4:34): R. Tam requires a proof only if he was established to be a Nochri. If not, he is believed through a Migo. He could have said that he is a Yisrael. Pesachim 3b connotes like this, and also the Beraisa in which R. Yehudah says 'you are believed to disqualify yourself, but your children are Kosher.' Even he himself would be Kosher had he not disqualified himself.

Question: Perhaps this is only where the majority are Yisre'elim (e.g. those who come to eat Pesach in the Mikdash)!

Answer (Tosfos 47a DH b'Muchzak, and Rosh ibid.): In all places, most who come b'Chezkas Yisrael are Yisre'elim.

Tosfos (ibid.): If one said that he converted without Beis Din, he is Kosher, but he forbids himself [to a Yisre'elis]. If he had Bi'ah with a Bas Kohen, he did not disqualify her. There is no proof from Rav Yehudah (45a, who counseled people to go to where they are unknown). Perhaps they would check if he is a Yisrael, but they would not check his family.

Rosh (ibid.): If witnesses say 'we heard that he converted in Ploni's Beis Din', this is a mere Giluy Milsa (revealing a verifiable matter). They are considered witnesses. Perhaps this is only according to R. Yehudah, who is lenient in Chutz la'Aretz. Perhaps Rabanan require a clear proof.

Question (Yam Shel Shlomo Yevamos 4:47, Korban Nesan'el 8): The Gemara asked what is the Chidush of the verse if he has witnesses. Rav Sheshes answered that the witnesses merely heard that he converted. I.e. all agree that "Ki Yagur" teaches this! They argue only about the verse "b'Artzechem."

Korban Nesan'el (8): Also, we learn from R. Yehudah to Chachamim. He requires a proof in Eretz Yisrael, yet witnesses who say 'we heard' suffice. Chachamim say 'also in Chutz la'Aretz he needs a proof.' They did not argue about witnesses who heard! Only R. Yehudah needed to expound Ki Yagur. From "Imach" (Hagahos ha'Gra 47a - this should say "Itchem", in the verse after Ki Yagur) we learn about one who is established to you, like from "Itcha". If so, how can we expound to require a proof only in Eretz Yisrael? Perhaps one needs a proof in both places! Verses are required for both of these. Had it said only 'ba'Aretz', one might have thought that we accept converts only in Eretz Yisrael. Had it not said 'ba'Aretz', one might have thought that we do not accept converts in Eretz Yisrael, lest they seek benefits (e.g. Matanos Aniyim). R. Yehudah expounds Ki Yagur to teach about one who has witnesses, in the most reasonable case, i.e. Chutz la'Aretz. Witnesses say that they heard they he converted in Ploni's Beis Din. R. Yehudah teaches that in Eretz Yisrael, one must bring a total proof. In Chutz la'Aretz, it suffices to have witnesses who heard. Chachamim require a total proof in Eretz Yisrael and Chutz la'Aretz. They do not expound Ki Yagur. It is normal for the verse to say this, since it says Itcha.

Poskim

Shulchan Aruch (YD 268:10): If a Nochri or Nochris comes and says 'I converted properly in Ploni's Beis Din, he is not believed to marry a Yisrael until he brings witnesses. If we saw him act like a Yisrael and observe all the Mitzvos, he is established to be a convert, even without witnesses in front of whom he converted. Even so, we do not marry him among Yisrael until he brings witnesses or immerses in front of us, since he was established to be a Nochri.

Gra (23): The Rambam (13:9) says that if we saw a convert acting like a Yisrael, e.g. she immerses after being Nidah and separates Terumah, or he immerses after Keri and does all the Mitzvos, he or she has Chezkas Yisrael. He learns from 45b. The Ramban disagrees. If so, the Gemara should have said "surely he observed one Shabbos"! It is easier to know this than Tevilah. The Yerushalmi says that if [one Muchzak to be] a convert circumcised but did not immerse, he is Kosher. Surely he immersed for Keri! Since he immerses for the sake of Kedushas Yisrael, it counts [for conversion].

Shulchan Aruch (ibid.): If one came and says 'I was a Nochri, and I converted in Beis Din, he is believed, for the one who forbade is believed to permit.

Shach (20): I.e. this applies only to one who was Muchzak to be a Nochri, and said that he converted. If he was not Muchzak to be a Nochri, and [said that] he converted in Beis Din, he is believed through a Migo. He could have said that he is a [native] Yisrael.

Gra (25): Migdal Oz brings this from the Yerushalmi. It says "Eretz Yisrael is dear. It is Machshir converts. In Eretz Yisrael we accept converts immediately, and in Chutz la'Aretz we require witnesses." This seems unlike the Bavli. We hold that in both [places he must bring a proof], and R. Yehudah holds oppositely! (He requires a proof only in Eretz Yisrael.) The Rambam explains that the Yerushalmi discusses such a case (he has a Migo). This is a stringency of lineage, like we say in Kidushin (69b. All lands are considered a dough, i.e. doubtful lineage, compared to Eretz Yisrael). The Yerushalmi holds like the opinion in the Bavli that also Bavel is a dough compared to Eretz Yisrael.

Shulchan Aruch (ibid.): The Rambam says that this is only in Eretz Yisrael when all there were Muchzakim to be Yisraelim, but in Chutz la'Aretz one must bring a proof before he may marry a Yisraelis. This is a stringency of lineage.

Bach (12): The Halachah follows Chachamim. R. Yehudah requires a proof only in Eretz Yisrael, lest he is a circumcised Giv'oni (a Kena'ani nation that converted through deception. Mid'Rabanan, they may not marry Yisraelim.) In Chutz la'Aretz, there is no benefit to say that he is a Yisrael, so surely he does not lie. Rather, even in Chutz la'Aretz he needs a proof. The Tur understood that the Rosh was unsure whether Chachamim agree that it suffices for witnesses to say 'we heard...' One should be stringent. It seems that also the Rif and Rambam are stringent.

Bach (DH u'Mah she'Chasav u'Mah, brought in Shach 21): Tosfos and the Rosh connote that we do not distinguish Eretz Yisrael [from Chutz la'Aretz], both then, when all were Muchzakim to be Yisre'elim, and nowadays that most are not Yisre'elim. He is believed even to marry a Yisraelis. Semag says that often guests come and we drink wine with them and drink what they slaughter. However, the Rambam requires a proof nowadays before marrying a Yisraelis. This is a stringency of lineage. The Shulchan Aruch brings this. However, the custom is to believe him even to marry a Yisraelis. Perhaps the Rambam agrees about guests who come b'Chezkas Yisrael. Even though most are not Yisre'elim, he is believed even to marry a Yisraelis, for all families have Chezkas Kashrus (EH 2:2). The Rambam discussed one whom we do not know that he was once a Nochri, and he says that he converted in Ploni's Beis Din. He is believed due to a Migo. Even so, we are stringent about lineage not to rely on the Migo to marry him to a Yisraelis without a proof. We rule like this.