Sounds to me like a great way to meet your neighbors. I'd catch him and carry him door-to-door to find out who he belongs to. (Ask the neighborhood kids, they always know where the pets belong). That way you could make sure his shots are up-to-date in case he still wants to hang around your place (obviously the word is out that you love animals). I'd let the owner know that he likes to visit you and ask them if that's okay with them. He's obviously well fed -- heck he might belong to several families and they're all feeding him. Kitties are smart. You have been chosen!