I didn't notice your question the first time I read your update, but here's your answer. x3
Like in the anime, pokeballs are (somehow automatically) registered to their trainers, and in order to officially trade one must use a trading machine. You'll be able to find those in the pokemon center. Unless the original owner reports a pokemon as stolen though, you won't get in trouble for just taking someone else's pokemon generally speaking. Alternatively, a trainer can release their pokemon (As in, permanently) but with the intention of the other trainer catching it.