To whom does the Tallit belong?

Last year, I was the Baal Koreh in my yeshiva, and I needed a tallit. I made an agreement with a third-year student who was a Kohen and had a tallit, that I would fold his tallit, and in return, I could use it on Mondays and Thursdays. Since then, I developed a sort of partial ownership of the tallit, and it turned out that I even used it more. At the end of the year, he collected phone numbers from several guys to contact them, including mine. I reminded him several times to take his tallit, but he didn't. Ultimately, the tallit has remained with me for 3 months now, and he never called to ask for it. He lives in another city, I have no idea where, and I tried to get his phone number but couldn't. Can the tallit now be officially considered mine, as if the owner has given up on it? He was a Breslov Hasid, and this has certain implications. Am I allowed to replace the tzitzit as if it were mine, or do I need to turn the world upside down to find him and not touch the threads of the tallit according to the law?

Shalom and blessings. You can use the tallit as you wish, and if he comes to claim his share in the tallit, you can pay him.

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