The dispute revolves over the question of whether "Kol d'Alim Gavar" represents a Halachic ruling, or a withdrawal from presenting a ruling. In other words do we accept that the more correct person will prevail and therefore we rule that it should remain by the winner, or are we saying that for the lack of proper evidence we leave the case unresolved (and therefore they can grab it from each other).

As for the Halachah, in general when the Halachic authorities dispute how to rule in a question of monetary law, the one holding the money can claim "Kim Li," meaning "to take the object away from my possession you must prove that the Halachah is with my opponent." Therefore if it was grabbed back it will remain by the grabber. However, if we saw him take it the Halachah may be different.

D. Zupnik

The Kollel had an Insights that delves into the argument between the Rosh and Tosfos a bit further. I include that here for your benefit.

M. Kornfeld

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1) THE LOGIC OF "KOL D'ALIM GEVAR"

OPINIONS: The Gemara teaches that in a case in which two litigants argue over the ownership of an object (such as a boat) which neither one of them is holding in his possession, the rule of "Kol d'Alim Gevar" applies, and whichever disputant overpowers the other prevails and gets to keep the object.

How are we to understand this apparently strange ruling in which Beis Din allows the two disputing parties to fight against and overpower each other?

(a) The RASHBAM (end of DH Hasam) explains that when it is possible that one litigant will bring proof to support his case, Beis Din does not rule "Yachloku" or "Shuda d'Dayani," because Beis Din might need to retract its ruling at a future time when proof is brought. Therefore, Beis Din does not get involved, but rather they leave the case alone and let the litigants contend with each other, and whoever is stronger will overpower the other until either one can present to the court proper proof of ownership.

The Rashbam's words imply that "Kol d'Alim Gevar" is not a Halachic ruling that Beis Din issues based on an analysis of the case. Rather, "Kol d'Alim Gevar" is a mechanism wherein Beis Din withdraws from the case and issues no ruling.

(b) The ROSH here (3:22), in Bava Metzia (1:1), and in Teshuvos (77:1) writes that there is some logic to the principle of "Kol d'Alim Gevar." He explains that, first, the true owner will probably bring proof to his ownership soon, as the Gemara explains, and therefore even if one overpowers the other, justice eventually will prevail. Second, it is probable that the true owner will overpower his opponent, because he will put more effort into claiming the object since he knows that it is his by right. The claimant who is not the true owner will not put forth so much effort to get the object, because he is afraid that the court will take it away from him later and give it to the other party based on proof of ownership that the other party will bring.

The Rosh adds that once one person overpowers the other, Beis Din no longer allows the two of them to physically seize the object from each other without sufficient proof of ownership, in order that they not continually be fighting with each other.

The SHITAH LO NODA L'MI (cited by the Shitah Mekubetzes) questions the Rosh's explanation. According to the Rosh, why should Beis Din get involved with the case and protect the rights of the first person who seizes the object? The Gemara teaches that Beis Din prefers to stay uninvolved with the quarrel and not pass judgement, and thus even when one litigant seizes the object, Beis Din should still stay uninvolved and not pass judgement! The Shitah therefore rules that Beis Din will not protect the seizure of the object by either party, and even after one party has seized the object, the other can grab it back and take it for himself.

It seems that the Rosh, who argues with the Shitah's view, understands the principle of "Kol d'Alim Gevar" differently. Rather than being a withdrawal of Beis Din from the case, Beis Din indeed is issuing a ruling on the case. As the Rosh himself explains, Beis Din is ruling that the one who overpowers his opponent is the true owner. Therefore, after one overpowers the other, Beis Din is entitled to become involved in order to uphold its ruling.

The CHASAM SOFER and CHIDUSHEI RABEINU MEIR SIMCHAH explain, based on this, a new way of understanding the Machlokes (on 34b) regarding whether Beis Din is allowed to return the object to the public domain, after Beis Din has appropriated the object in order to give time to the true owner to bring proof of ownership, and allow the litigants to fight over the object. Rav Yehudah, who says that Beis Din may not remove the object from the domain of Beis Din, maintains (like the Rashbam) that "Kol d'Alim Gevar" means that Beis Din withdraws from the litigation. Beis Din has no right to withdraw, though, once it has already taken the object into its custody, as the Rashbam explains there. Rav Papa who argues and says that Beis Din can return the object maintains that "Kol d'Alim Gevar" is also a form of justice, and therefore Beis Din may take the object out of its custody and say "Kol d'Alim Gevar," being assured that justice will be done.

However, there are some questionable points on this understanding of the Rosh. First, the Poskim cite the Rosh's ruling l'Halachah, even though we also rule that "Lo Mafkinan" -- once the object is in the custody of Beis Din we do not take it out of Beis Din's custody and say "Kol d'Alim Gevar."

Second, if the Rosh indeed is proposing a logical reason to explain why the one who grabs the object is probably the true owner, then why should that logic not apply after the first time the object is seized by one of the disputants? If the second disputant later overpowers the first and takes the object from him, then it should show that he is the true owner and not the first one!

Third, the Rosh himself in Teshuvos (loc. cit.) seems to contradict his explanation. Although he repeats what he writes in our Sugya, he writes that "Kol d'Alim Gevar" is not a "Din," a formal ruling of Beis Din, but rather it is merely the withdrawal of Beis Din from the case ("Histalkus"), where Beis Din declines from issuing a ruling! He proves this first from our Gemara, which says that the reason we rule "Kol d'Alim Gevar" is because one defendant might eventually bring a proof, and therefore it is not necessary for Beis Din to pass a ruling. This implies that "Kol d'Alim Gevar" is the act of refraining from issuing a ruling. (See also KOVETZ SHI'URIM who asks this question without citing the Teshuvah of the Rosh.)

In addition, RABEINU CHANANEL (cited by Tosfos and Rashbam on 34b) writes that we do not apply "Kol d'Alim Gevar" when the disputants are holding the object, because Beis Din has no right to take the object out of someone's hands when it does not know who owns the object. This again implies that "Kol d'Alim Gevar" would not determine the identity of the true owner of the object. The Rosh, based on these proofs, therefore rules that when one party overpowers the other, the losing party is entitled to force the winning party to swear with a "Shevu'as Heses" that the object is his.

Based on what the Rosh in Teshuvos writes, it seems that the Rosh here should be understood differently. The Rosh agrees that "Kol d'Alim Gevar" is a means for Beis Din to withdraw from the case. However, the Rosh was bothered by a question: how can Beis Din -- the role of which is to maintain peace and order in the community (Bava Metzia 96b) -- remove itself from the case and refrain from maintaining the peace, allowing chaos to prevail? The Rosh therefore proposes two complementary suggestions. First, the court will stop the free-for-all after the first seizure of the object, and consequently peace will be restored. Second, even the first seizure has some logical basis in determining the ownership of the object, since we may assume that the one who prevailed over his opponent is the true owner. (M. Kornfeld)