So there are three dragons and legends point to three dragon riders. We can assume Dany is one of them, but who are the other two? I think it's (not going out on a limb here) two of Tyrion/Bran/Jon.

 

Tyrion - There is a theory out there that "A+J=T" and Tyrion is the son of Aerys II and Joanna. If so, he's for sure riding a dragon. Even if he isn't, I could see him riding one given his infatuation with dragons and being the one who released them.

 

Jon Snow - R+L=J is virtually a lock at this point. Jon being a Targaryren and the probably Azor Ahai gives him dragon riding equity.

 

Bran - Bran is definitely a Stark and I don't see him riding a dragon, per se. However, he is en route to becoming the most powerful warg of all time. That, and two comments from the bloodraven ("You will never walk again, but you will fly", "You won't stay here forever") make it possible that he wargs into one of the dragons.

 

 

 

What I see (or hope) is that Dany rides Drogon, Tyrion rides Rhaegal, and Bran wargs into Viserion. Jon, despite being Targaryen, chooses to lead the ground attack rather than riding a dragon.

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