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Given the following post, respond as if you're commenting on Reddit:
human
[Game of Thrones/ASOIF] (Spoilers) What are everyone's claims to the Iron Throne, and which ones have weight by law?

Please include claims from anyone alive at the start of the series.
gpt
I'll start at the death of Robert Baratheon. 

Joffrey is believed to be Robert's eldest son, so he would hold the most right in the eyes of the law, if true. Even though he is not in fact blood, he's still thought to be his son. Obviously him not being his son makes his claim moot. 

Viserys and by extension Daenarys have their claims built on the back that Robert stole the throne from their father, Aerys. And they are willing to take it back from his family. 

Both Stannis and Renly make their claims acknowledging that Joffrey, Tommen, and Myrcella are incestual bastards, unrelated to Robert.

Stannis is the second eldest brother, only younger than Robert himself, and since Joffrey as well as none of his siblings are Baratheons he has the strongest claim to the throne. This is because he's his closest living relative. 

Renly is Robert's youngest brother, and acknowledges that Stannis should be before him.  However since he's more well liked and Stannis is very rigid he thinks he should be king.

Robert has a bunch of bastards who could make a claim, but would likely be ignored.