Gemara

61b (Mishnah - Beis Hillel): A man may not neglect having children unless he has children. He must have a male and a female.

62a (R. Yochanan): If a Nochri had children and then converted, he fulfilled Peru u'Rvu (because he had children);

Reish Lakish says that he did not fulfill it (because a convert is like a newborn).

Question (R. Yochanan): "Bradach Bladan ben Bladan..." (this shows that their children are considered children)!

Answer: (Reish Lakish): While they are Nochrim they have lineage. When they convert, they lose it.

They argued similarly elsewhere:

(R. Yochanan): If A Nochri had children and then converted, his first son born after conversion is not considered a Bechor, for he has previous sons;

Reish Lakish says, he is a Bechor, since a firstborn Nochri has no special law of inheritance.

It was necessary for R. Yochanan and Reish Lakish to argue in both cases.

Had they argued only in the first case, one might have thought that R. Yochanan argues only there, because Piryah v'Rivyah also applies to Nochrim, but regarding inheritance he would admit to Reish Lakish;

Had they argued only in the second case, one would say that Reish Lakish argues only there, but regarding Peru u'Rvu he would admit to R. Yochanan.

Question (R. Yochanan): "Bradach Bladan ben Bladan..." (shows that they have lineage)!

Answer: (Reish Lakish): While they are Nochrim they have lineage. When they convert, they lose it.

(Rav): All agree that a slave has no lineage. "Shevu Lachem Po Im ha'Chamor" - ("Im" connotes equality, and it can be read 'Am', i.e.) a nation like a donkey. (Therefore, if a slave had children and converted, he did not fulfill Peru u'Rvu.)

Question: "To Tziva (Mefivoshes' slave) were 15 Banim and 20 slaves".

Answer (Rav Acha bar Yakov): This does not connote lineage any more than "Par Ben Bakar" (a bull born to cattle).

Question: If so, the same applies to Nochrim!

Answer #1: Regarding Nochrim, it specifies the names of the son and the father. Regarding slaves, it does not.

Answer #2: Elsewhere, a Nochri is traced to his father and grandfather - "Ben Hadad ben Tavrimum ben Chaziyon."

(Beraisa): If a child died or was found to be a Seris, his father did not fulfill Peru u'Revu.

63b (Rav Asi): "Ki Ru'ach mi'Lefanai Ya'atof (souls in front of Me delay)" - (Moshi'ach) the son of David will not come until all Neshamos in 'Guf' (a treasury) are completed.

Rishonim

Rif and Rosh (6:7): The Halachah follows R. Yochanan, who says that if a Nochri had children and then converted, he fulfilled Peru u'Rvu.

Rambam (Hilchos Ishus 15:4): A man must have a son and a daughter to fulfill Peru u'Rvu. If the son was a Seris or the daughter was an Ailonis he was not Yotzei.

Source (Magid Mishneh): A Beraisa says that one is not Yotzei with a Seris, and the same applies to an Ailonis. The Yerushalmi (6:6) says so explicitly.

Rambam (6): If a Nochri had children and he and they converted, he fulfilled Peru u'Rvu. If a slave had children and he and they were freed, he was not Yotzei until he has children after being freed, for a slave has no lineage.

Magid Mishneh: Had the Nochri's children not converted, he would be obligated to have children Yisraelim.

Maharil (Teshuvah 196): There is no reason why one is not Yotzei Peru u'Rvu with a child who is a Cheresh or lunatic. We hold like R. Yochanan, who says that a convert is Yotzei with children he had before conversion, even if the children did not convert. Reish Lakish argues only because a convert is like a newborn. If Peru u'Rvu is due to Lasheves Yetzarah, this is fulfilled for the child can marry and have healthy children. If we are concerned for finishing Neshamos from the storehouse this is fulfilled. Mitzvos apply to even to a Shoteh. Others are commanded that he not transgress (they cannot make him transgress). If healthy people saw him slaughter it is Kosher, unlike a Nochri or animal that slaughtered. He can do Yibum. One may not curse him.

Poskim

Shulchan Aruch (EH 1:5): Once a man has a son and a daughter he fulfilled Peru u'Rvu, provided that the son is not a Seris and she is not an Ailonis.

Chelkas Mechokek (6): If Levi's children did not get married, or married a Seris or Ailonis, Levi was Yotzei. If not, the Shulchan Aruch would have taught this bigger Chidush.

Rema (6): If the child was a Mamzer, Cheresh, lunatic or child, he was Yotzei.

Source (Beis Yosef DH Garsinan): The Ritva (22a DH Masnisin) explains that the Yerushalmi (2:6) says that one is Yotzei with a Mamzer. The Maharil (cited above) says that one is Yotzei with a Cheresh or lunatic.

Gra (16): The Mishnah (2:6) says that 'a child from anywhere is considered a child' includes a Mamzer regarding Peru u'Rvu. It did not need to say that a Cheresh or lunatic is considered a child.

Beis Shmuel (10): Sefer Chasidim says that one is not Yotzei with a Mamzer, for he will not live. Perhaps this refers to an unknown Mamzer, but a known Mamzer lives (Yevamos 78b), so one is Yotzei with him.

Shulchan Aruch (7): If a Nochri had children and he and they converted, he fulfilled Peru u'Rvu. If a slave had children and he and they were freed, he was not Yotzei until he has children after being freed.

Chelkas Mechokek (9): The Maharil (196) says that he was Yotzei even if the children did not convert. The Gemara supports this.

Gra (17): The Rambam explains our Sugya to discuss when also his children converted. He explains 'at first, inheritance does not apply to them' simply. I.e., before the children convert they do not inherit their father who converted. Rashi and Tosfos must explain that this means that before conversion, inheritance of a Bechor does not apply. However, the Gemara in Bechoros (47a) is unlike the Rambam. It assumes that the case of inheritance resembles the case of Peru u'Rvu, and there is no source to say that we discuss when the children converted! All the Poskim are unlike the Rambam.

Chelkas Mechokek (8): It is not clear whether or not a man fulfills Peru u'Rvu with children born (not through Bi'ah, e.g.) from his semen left in a bathhouse (and a woman sat on it. It seems that he is Yotzei, for) Avodas ha'Kodesh calls Ben Sira the son of Yirmeyahu even though he was born in this way.

Beis Shmuel (10): The SMaK says that a woman should avoid sitting on another man's semen, lest a man marry his paternal sister. This implies that the child is considered his father's son, so he counts towards Peru u'Rvu.