Okay, so I have a zombie deck that has Grave Betrayal in it. I have several cards in my deck that return zombie cards from the graveyard to the battlefield/my hand. My question is when an opponents creature dies and it comes to the battlefield under my control and then that creature dies while under my control, does it go to my graveyard or back to theirs?
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"Silence rules Bala Ged, broken only by the skittering of Eldrazi."
Cards you own will always go to your hand, library, graveyard, and exile. You will never have anyone else's cards in your graveyard (or library, hand, or exile).
Yes. It goes to its owner's graveyard, always, and you're not the owner.
Correct. The specific rule is
400.3. If an object would go to any library, graveyard, or hand other than its owner’s, it goes to its owner’s corresponding zone.