Harry Potter, the ending?

Harry was the owner of the Elder wand, yes. Harry had a wand beneath his cloak as he went into the Forest. When Voldemort struck Harry down, it didn't kill Harry, it destroyed the Horcrux, which was a piece of Voldemorts soul. Also, when he attacked Harry, it didn't disarm him. So therefore, Harry still had rightful ownership of the wand.

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no because Voldemort was using the elder wand, not using another wand against the elder wand. I don't think you can defeat the elder wand and become it's ower by using the actual elder wand.

and Harry wasn't fully dead then either

Harry didn't try to defend himself, so the Elder Wand didn't recognize Voldemort as having beaten him.

It was my understanding that Harry never actually wanted the Elder Wand.

The only thing I remember him doing with it is repairing the wand he had to begin with.

Harry never truly died, he was just unconscious, and hallucinating (by seeing Dumbeldore) so he was never rele dead, therefor he was still the owner of the elder wand wen he disarmed malfoy. thats also how malfoy got the wand, which was by disarming dumbeldore. but then wen harry disarmed malfoy, he became the new owner of the wand. and since he had malfoys wand with him, but was never disarmed or killed, he was still the owner of the elder wand. he sacrificed himself for the protection of his friends, he never rele died, but the horcrux that was in him died. so wen voldemort used the avada kadavra curse on harry, he wasnt killing harry, but he was killing the horcrux inside of him. thats y wen harry was unconscious (due to the powerful curse) there was a thing that kept whimpering and crying. that was the horcrux that was dying from the curse. basically, the horcrux took the effects of the curse, and not harry. he was just unconscious, not dead, because of the curse and the strength the curse had. so since harry was never disarmed, or killed, he was never defeated, and therefor was still the true owner of the wand

Harry wasn't born with the Elder wand. He wouldn't have had a wand as a baby. Dumbledore had the wand :D

No, because he didn't actually kill Harry. He only destroyed the Horcrux that was inside him; it acted as a sort of shield, saving Harry's life.

he didn't die so it still belongs to him.

No. The aliens did it.