Except for the Pokemon Ash releases or gives to another trainer, he's not giving up ownership. They're still his Pokemon when left at Professor Oak's lab. After the original series (seasons 1-5) they've made it so Ash resets his team except for Pikachu. For the show it's so he can catch the Pokémon of that region, but really it's to advertise the new Pokémon for the new games that accompany the new season. There are times early on that it would make sense for Ash to keep at least some of his Pokémon because of Team Rocket stealing Pikachu, but once he gets new ones he doesn't really need them. I liked it more that Ash's Pokémon got actual goodbyes during Johto then him just leaving them behind at the end of the series, but at least they occasionally brought back his older Pokémon at one time and another in each later series.
