Gemara

15b: Since half-damage is a fine, if a dog ate a (large) sheep, this is abnormal (hence a Toldah of Keren), so we do not collect it in Bavel (like all other fines). If the victim seized payment, we do not make him return it.

74b (Beraisa): Once, R. Gamliel told Yehoshua 'I blinded the eye of my slave Tavi.' R. Yehoshua said 'he does not go free, for you have no witnesses.'

Inference: If he had witnesses, Tavi would go free, even though R. Gamliel already admitted. His admission did not exempt because he did not admit in front of Beis Din, or because it was not in Beis Din.

84a: Once, an ox chewed the hand of a child. Rava commanded to evaluate what he would be sold for like a slave.

Question (Rabanan): You taught that in Bavel we do not collect anything that requires an evaluation of one's slave value!

Rava: I did not say that the damager must pay this. Rather, if the victim grabs payment, we must know how much he may keep.

Rishonim

The Rif and Rosh (6a and 30a, 1:20 and 8:2) bring the Gemara.

Rosh: The Rif's text says that we evaluate now, in case the victim will seize. This is wrong. We evaluate only if the victim seized. Some texts say like this.

Rosh (1:20): Even though half-damage is a fine and we do not collect it in Bavel, if the victim seized, he need not return it. R. Tam says that Chachamim were lenient about this only if he seized the damager itself at the time of the damage. If one may seize anything and need not return it, this would lead to disaster. People will steal everything from one another, since we do not take it back, since we do not judge fines in Bavel. One will lose more than he damaged!

Hagahos Ashri (8:2): Or Zaru'a says that R. Tam says that the same applies to other Avos Nezikim, e.g. Shen, Regel, man, fire, a pit, the four Shomrim, healing, unemployment, Boshes due to damage, a Ganav (to pay principal) or Gazlan, Edim Zomemim when the money cannot be returned, and Moser. Mahari'ach was unsure about fire and a pit.

Rosh: R. Tam is difficult. If one took more than the damage, Beis Din can judge the case to make him return the excess! This is not called judging fines, for he already collected the damage through the enactment. We judge only to return the excess! Rather, no matter what he took, we do not remove it. If he took more than the damage, we judge the case and make him return the excess.

Rosh (ibid., citing the Ra'avad): Seizure does not help if he admitted, even if he seized before he admitted. A slave is like one who seized himself, yet R. Gamliel's admission stopped Tavi from going free (74b)!

Rosh (ibid., citing the Ramban): Admission exempt only in Beis Din (74b)! An ox cannot become Mu'ad in Bavel (84b), for there is no Beis Din of judges with Semichah. Likewise, nowadays there cannot be admission in Beis Din. Therefore, we do not take from one who seized before or after admission. A case occurred (19b) in which Rav Yehudah obligated half-damage (a fine); we must say that this is if the victim seized, or summonsed him to trial in Eretz Yisrael. Nowadays we do not summons, for there are no Semuchim even in Eretz Yisrael.

Rosh: The Ramah says that seizure helps only up to the value of the damage. If one seized more, e.g. Kefel, four or five, we remove it. Chachamim allowed keeping only up to the value of the damage. Also, it is an enactment that seizure helps. Chachamim enacted only up to the damage, so the victim will not lose, but not that he should profit from others' money.

Rebuttal (Rosh): It is mid'Oraisa law, just no judge in Bavel can enforce it. Therefore, the victim may take the law into his own hands. We do not remove up to what the damager owes mid'Oraisa. If the victim says 'accept my (witnesses) testimony, so if I will seize, you will not take it from me', we do not accede, for we do not collect fines in Bavel. This is why there is no Mu'ad in Bavel. If the damager says that he seized too much, we accept testimony to judge this. If he cannot bring proper testimony, he must return it.

Rambam (Hilchos Sanhedrin 5:9): Judges in Chutz la'Aretz judge only common things that entail monetary loss, e.g. admissions, loans, and property damage.

Rambam (17): Even though we do not collect fines in Chutz la'Aretz, if the victim seized the proper amount, we do not take it from him.

Hagahos Maimoniyos (7, citing R. Baruch): R. Tam holds that even Tefisah of the damager itself helps only right after the damage, before it comes to the owner's hand. We find that R. Tarfon holds that Tefisah helps after death; Rav and Shmuel say that it helps only in Reshus ha'Rabim (Kesuvos 84b).

Poskim

Shulchan Aruch (CM 1:5): Judges without Semichah in Eretz Yisrael cannot collect fines in Bavel. However, if the victim seized the proper amount, we do not take it from him.

SMA (18): We do not take it from him even if he seized Kefel, four or five. R. Tam allows seizing only the damager, and only immediately. The Mechaber says Stam that Tefisah helps, like the Rosh. The Mordechai rules like R. Tam regarding Nezek of Keren (goring or anything unusual), and like those who disagree regarding other damages. The Mechaber did not say that Tefisah does not help after admission. He holds like the Ramban, who says that admission exempts only in front of Semuchim, which we do not have.

SMA (19): The Tur says that if one seized and cannot bring witnesses (that he was owed), he must return it. The Maharshal says that if witnesses did not see him seize, he is believed Migo (since) he could say that he did not seize.'

Rema: If the victim says 'assess the damage, so if I will know how much I may seize', we do not accede.

Gra (24): According to the Rif's text, we accede. Also Rashi says so.

Shach (17): In something that is not a fine, the Maharshal rules like the Rif, that we assess to enable him to seize.

Shulchan Aruch (ibid.): If he already seized, we assess and say 'this you may keep; return the rest.'

Darchei Moshe (6): Binyamin Ze'ev (132) says that even though nowadays admission in Beis Din does not exempt if witnesses come later, it does not obligate if witnesses do not come (if the victim seized, we take it from him). Perhaps the Ramban disagrees.

Taz: Tefisah helps even in front of witnesses. It is not so he will be believed (through a Migo). Rather, one who seized does not need judges. He takes the law into his own hands.

Rema (CM 348:4): The Mechaber did not teach when a Ganav pays four or five because it is a fine and does not apply nowadays. However, it is relevant if the victim seized the money.

SMA (11): Perhaps the Mechaber holds like the Ramah, that it is an enactment that seizure helps. Chachamim enacted only up to the value of the damage. The Rema holds like the Rosh, that it is mid'Oraisa law, hence even if he seized the full Kefel or four or five, he need not return it.

Gra (18): The Gemara supports the Ramah. We find only that half-damage was collected in Bavel through seizure, but not Kefel. It is an enactment that seizure helps. Chachamim enacted only up to the value of the damage. The Rema holds like the Rosh, that it is mid'Oraisa law, hence even if he seized the full Kefel or four or five, he need not return it.