Board Thread:Questions and Answers/@comment-202.80.217.27-20160620145143/@comment-5014364-20160626164706

Jman321 wrote: No, the Baratheons are distant bastard relatives of the Targaryens. The founder of House Baratheon was Orys Baratheon and he was Aegon "The Conqueror" Targaryen's bastard half-brother.

It was only rumored that Orys was a Targaryen bastard. The Baratheons later intermarried with the Targaryens in a formal marriage: in the books it was the grandmother of Robert/Stannis/Renly and thus Aemon's niece. TV show may have condensed this to be just his mother.

Practical result is that Gendry is part Targaryen.