Forum:Blast Sphere/Worm Milidith

When the effects of Blast Sphere and Worm Milidith activate, do they change ownership and go to your opponent's side of the field and into their spell and trap zone? If so, what happens if your opponent has a full spell and trap zone? Would it destroy one of those cards?

If it does not change ownership to them, where does it go? Does it stay as a monster on your side of the field in face-up defense, or revert to your spell and trap zone?