Mainly just putting it in these tags because of maybe some not hearing the theory of Tyrion also being of part Targaryan. So firstly, in the finale, when watching the dragons fly, one of them DID seem smaller than the other two, and there's a theory that, like the Dire Wolves, each dragon is meant for someone. And with Tyrion talking about always wanting a dragon, since he was a little kid, the smallest dragon could be for him. As the third Targaryan.
Then there's the scene of lyanna stark in the flashback and that she was dying after childbirth. Same as Tyrions mother, and same as Daenerys was when giving birth but gave birth in a tent where magic was being done. I don't know all of the history, but my theory is of women giving birth to non-100% Targaryan's die after child birth, and possibly Daenerys lived because either she is Targaryan and only non Targaryan women die because of not being able to handle such pain, or because of the magic going on in the tent that she was placed in saved her.
It's a bit out there for theories, but it's so far the only evidence I came up with to support this fan theory. What do you think?