This is the subject of a dispute between the Rishonim.

1) It appears from the Rosh here, at the beginning of Bava Metzia #1, that it is a Psak. The Rosh writes concerning the boat that since the Beis Din does not know to whom it belongs, and no one is in possession of it, the Beis Din does not have to stop someone who comes along and grabs it. Indeed, if the Beis Din would give it to one of the contestants, Beis Din might be causing the rightful owner to lose his property unjustly. Therefore, Beis Din tells the two litigants that from the fact that one of them prevails (either physically, or legally -- in that he manages to produce better proofs for his position in court), we may assume that he is the rightful owner. The Rosh adds that we assume that the real owner will show more self-sacrifice to retain his own legal possessions than a thief will show in order to steal.

2) What is apparent from the words of the Rosh is that the Beis Din is seeking a way of issuing the correct ruling. Beis Din cannot get involved directly and decide to whom it belongs, but by saying "Kol d'Alim Gavar" we hope that this will be a way of finding out who the real owner is, because he is more likely to make a greater effort to make sure he retains ownership of his possessions. If the opinion of the Rosh would have been that Beis Din is merely taking themselves off the case, it would not have been necessary for him to write that through Kol d'Alim Gavar it is more likely that the true owner will win out.

3) What is the Din if, after A grabs it, B succeeds in grabbing it back from A? The Shulchan Aruch (CM 139:1) rules in the name of the Rosh that the Beis Din does not allow B to grab it back from A. However, the Shach there (#2) writes that according to Tosfos, Bava Metzia 6a, DH v'Ha, it clearly appears that Beis Din allows B to keep it. The Birkas Avraham on Bava Metzia 6a, page 41 (by Rav Avraham Erlanger shlit'a of Yeshivas Kol Torah, Yerushalayim) writes that the accepted way of explaining the dispute between the Rosh and Tosfos is to say that according to the Rosh, the Din of Kol d'Alim Gavar is a "Hachra'ah" -- a decision, a Pesak, while according to Tosfos it is a "Siluk" -- Beis Din merely removes themselves from the issue.

4) Therefore, according to the Rosh, when A grabs the ship this means that it proves that he is the rightful owner and it is considered that Beis Din has ruled as such. Since Beis Din has made such a Psak it is not possible to retract, in the same way that Beis Din does not usually retract on rulings that they have made. When B grabs it from A it is similar to grabbing an item from a person who has been granted an item by Beis Din, in which case we take the item away from the grabber. This is the opinion of the Rosh. However, according to Tosfos, Kol d'Alim Gavar is a Siluk -- we are simply not getting involved, but we are not claiming that we have decided anything. Therefore, if B grabs it back, Beis Din again does not get involved because they have taken themselves off the case and they allow B to keep it.

Kol Tuv,

Dovid Bloom