Originally Posted by Ph8te
Which could lead back to the comment "The seed is Strong" or something like that. Since the King has many children they all have claim to the throne of he is done away with.
No, they really don't. As we know from Jon Snow, bastards can't inherit -- not a family name or property. Jon Arryn's investigation wasn't intended to find a new heir, but just to try to determine the likelihood that Cersei's kids weren't Robert's.
In theory, if Robert died without a legitimate heir, his brother Stannis (who we haven't seen yet, but was mentioned this week by Renly as being older than him) would be next in line.
As things currently stand, as Renly mentioned, he is 4th in line -- after Joffrey, Tommen (the younger boy), and Stannis.