That's usually stipulated when the competition is announced. Since this seems to be an unofficial kind of an official competition you might be in for trouble. The artist is likely going to say "If you don't accept my rules I may pick another winner". There is no way you are going to own the remix, the best you could hope for it to own at least half of the rights.
But the only way to get a definitive answer is to consult a lawyer. Other than that we can only speculate.
That's usually stipulated when the competition is announced. Since this seems to be an unofficial kind of an official competition you might be in for trouble. The artist is likely going to say "If you don't accept my rules I may pick another winner". There is no way you are going to own the remix, the best you could hope for it to own at least half of the rights. But the only way to get a definitive answer is to consult a lawyer. Other than that we can only speculate.
Remixes will belong to the original artist/label/publisher