Gemara

(Chizkiyah): "He will calculate (the redemption) with the one who bought him", not with the buyer's heirs.

(Rava): The Torah needed to teach that a Nochri does not inherit his father's slave. This shows that a Nochri inherits his father mid'Oraisa. A convert does not inherit his father mid'Oraisa, only mid'Rabanan;

(Mishnah): If a convert and a Nochri (his brother) inherited their father (a Nochri), the convert may tell his brother 'take the idols, and I will take the money. If the convert already received the idolatry, he may not trade it.

If a convert inherited mid'Oraisa, even before he receives it, it would be (half) his. It would be forbidden to trade it, for this is benefit from idolatry!

Conclusion: Rather, he inherits mid'Rabanan. This is a decree, lest he revert l'Suro (to being a Nochri).

Support (Beraisa): One can say 'take the idols, and I will take the money' when splitting an inheritance. A partner with a Nochri may not say this. A Nochri or a convert do not inherit a convert, not mid'Oraisa nor mid'Rabanan.

(Mishnah): If Reuven borrowed money from Yisro, a convert whose children converted with him, and Yisro died, Reuven should not return the money to Yisro's children. Chachamim are upset if he does.

Contradiction (Beraisa): If he returns to them, Chachamim are pleased!

Answer: We distinguish between when their mother converted before or after their birth.

(R. Chiya bar Avin): We learn that a Nochri inherits his father from "I gave Ar for an inheritance to the descendants of Lot".

Bava Kama 38a (Beraisa): If a Yisrael's ox gored a Nochri's ox, he is exempt. If a Nochri's ox gored a Yisrael's ox, even a Tam pays full damage. It says "va'Yater Nochrim." (This is like v'Hitir, He permitted their money to Yisrael.)

113b (Beraisa - R. Pinchas ben Ya'ir): If desecration of Hash-m's name will result, even keeping a Nochri's Aveidah is forbidden.

Bava Basra 149a: Isar converted between the conception and birth of his son Mari. (Isar had no heirs.) Isar had deposited money with Rava. Before he died, Isar wanted to give it to Mari, who was away learning.

Rava: Mari does not inherit Isar. Isar has no way to give the money to Mari!

Rav Ika brei d'Rav Ami suggested that Isar can admit that the money belongs to Rav Mari, and Rav Mari will acquire through Odisa ((even a false) admission)! This occurred. Rava was upset that someone told him, causing a loss to Rava.

Rishonim

The Rif and Rosh (1:22) bring our Sugya

Rambam (Hilchos Avodah Zarah 7:5 and Ma'achalos Asuros 13:22): If a convert was a partner with a Nochri, he may not say 'take the idols, and I will take the money.' He may say so when splitting an inheritance. This is a leniency given to a convert who inherits, lest he return to his rebellious way (being a Nochri). Once the idols came to his Reshus, he may not say so.

Rambam (Hilchos Nachalos 6:9): Mid'Oraisa, a Nochri inherits his father. Regarding other inheritances, we let them follow their custom.

Rambam (10): A convert does not inherit his Nochri father. Chachamim enacted that he inherits like he used to (before converting), lest he revert to his rebellious way. It seems that a stipulation works for this, since he is not obligated to fulfill Chachamim's enactment. A Nochri does not inherit his father who converted, and a convert does not inherit a convert, mid'Oraisa or mid'Rabanan.

Rosh (24): Rashi says that if a convert was born but not conceived in Kedushah (after his parents converted), one should return the money. Why didn't Rava want to give the money to Mari? R. Tam answers that a deposit is unlike a loan; Rava owed no gratitude to Isar. Alternatively, Mari's mother was a Yisraelis, so even according to Nochri law, Mari would not inherit Isar if they both reverted to be Nochrim. (We follow the mother.)

Ri (in Tosfos 18a DH Kan): If a convert was born but not conceived in Kedushah, one should not return the money, lest people think that he is a full Yisrael.

Poskim

Shulchan Aruch (YD 146:4): If a convert and a Nochri inherited their Nochri father, the convert may say 'take the idols, and I will take the money.' He may not say so after the idols came to his Reshus.

Shulchan Aruch (CM 283:1): Mid'Oraisa, a Nochri inherits his father. A convert does not inherit his Nochri father, just Chachamim enacted that he inherits like he used to (before converting), lest he revert to his old way.

Beis Yosef (DH u'Mah she'Chosav): A convert does not inherit his Nochri father mid'Oraisa, for his lineage does not follow his father's. He is like a newborn baby. He inherits mid'Rabanan, lest he revert l'Suro in order to inherit.

Prishah (2): Rashi (Horayos 13a) explains that Suro is his Yetzer Ra.

Shulchan Aruch (ibid.): A stipulation works for this, since the Nochri need not fulfill Chachamim's enactment.

SMA (4): The Nochri can uproot the inheritance by saying that Joe will inherit him, even if Joe is not an heir.

Taz: A Yisrael can do so only if he gives a gift. A Nochri can do so even if he calls it an inheritance.

Shulchan Aruch (ibid.): A Nochri does not inherit his father who converted, and a convert does not inherit a convert, mid'Oraisa or mid'Rabanan. Even if he had a son born but not conceived bi'Kedushah, he does not inherit his father, nor vice-versa.

Rema: If a Yisrael owed a Nochri, and the Nochri died, if Nochrim do not know about the debt, he need not return it to the heirs.

Source (Mordechai 491): Mar Rav Tzedek wrote that if a Nochri deposited with or lent to a Yisrael, if the Nochri died and the Yisrael does not return it to the heirs, he sins. Avi ha'Ezri says that this is only if the heirs or others know that he owes. Since they claim from him, it is Gezel (robbery). If not, it is not. Gezel is only taking by force - "va'Yigzol ha'Chanis mi'Yad ha'Mitzri."

SMA (6): If the heirs know, this is Gezel Nochri, which is forbidden. If they do not know, we apply "va'Yater Nochrim." This is unlike Ir Shushan, who says that if they know, we must return to avoid Chilul Hash-m.

Rebuttal (of SMA - Taz): Gezel does not depend on their knowledge.

Gra (1): Bava Kama 113b forbids if they know. See Rema (348:2). (Some permit to deceive a Nochri about a calculation or uproot his loan, provided that he will not know, and there will not be Chilul Hash-m. Some forbid to deceive him, but permit if he erred by himself.)