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[Skyrim] Who gets the claim on Dragonborn's soul?

During his or her adventures, Dragonborn has a lot of opportunities to become a servant or a champion of various Daedric Princes, including rather damning ones with Boethiah, Mephala or Namira. 

So if Dragonborn becomes a servant/champion of several or all Daedric Princes, who gets the soul? Or if we assume that Dragonborn indeed has a soul of a dragon, Akatosh gets the first and final claim?
gpt
There is no "assuming" the idea of the last dragonborn has a dragon soul. Their soul is 100% dragon but their body is mortal. It's the fundamental fact of any dragonborn, no matter their history or race. So no matter what petty daedra ends up beating its brothers/sisters to claim the soul, they have nothing on Akatosh's ultimate claim to his child once it leaves the mortal world. 

Not only that, but in order to defeat Alduin, the dragonborn must fight in Sovngarde, and gain the allegiance of all the honored dead who rest there. So if a daedra comes calling, it might have to deal with the legions of countless honored warriors who owe their very existence to the dragonborn. At the very least, they would fight to preserve the natural cycle and allow Akatosh to claim the dragonborn upon death. Or they may fight the daedra in order to let the dragonborn choose whoever they wish to spend eternity with. 

Also, let's not forget that sometimes daedra like to speak large but not deliver on their promises. They might like to say they own a person's soul or the destiny, but sometimes it's just so they can sound more intimidating or "godly" to the hapless person they're speaking to. Often they're not actually interested in claiming a soul, or sometimes don't have the power. Granted, the dragonborn is a very unique circumstance and any daedra worth their salt might still want that soul even if they usually don't keep mortals. But the fact is not all of them actually damn people, and sometimes they just talk to hear themselves talk. Often enough, a mortal spreading chaos or strife with their favorite weapon is enough for them, and they're content to let it slip back into history when their latest toy passes away.