The Targaryens have a very incestuous family tree. Lots of brother/sister/cousin marriages in that twisted lineage.
So who do you think is the 3rd Targaryen in the current story? The dragon has 3 heads, and all (the Targaryen sigil is the 3-headed dragon, Aegon The Conqueror united the 7 kingdoms with his 2 sisters, on the backs of 3 dragons). So far we have Dany and Jon, I'm wondering who the 3rd one will be that'll ride that 3rd dragon.
I read a fan theory yesterday that on its surface sounds stupid. But there were some interesting things to support it. It posited that Tyrion Lannister is the 3rd Targaryen. It's stupid on the surface because we already have his backstory about his mom dying in childbirth and that's why his sister and dad hate him so much. But maybe they hate him because they secretly know (er, knew in Tywin's case) that he's not in their blood line?
- Notice that Dany's dragons didn't harm him when he went to the dungeons to free them
- Tywin explicitly said "you're no son of mine" right before he took a crossbow dart to the heart
- The red witch in Essos (or Pentos or wherever he and Varys stopped on the way to Mereen) picked Tyrion out of the crowd, as if she sensed his presence. The red witches seem to have a sixth sense when it comes to picking out Targaryen blood...
- Dany, Jon, and Tyrion all had mothers that died during childbirth
- The incestuous nature of the Targaryen family tree made it common for them to suffer from madness (Aerys "the mad king") and deformities (maybe a certain dwarf?)
It's not exactly a strongly supported theory, but if not Tyrion, then who?