In A Clash of Kings, there has developed a situation where all of the powerful regions of the Seven Kingdoms are vying for control of the one main seat of power. The true heir to the throne, Daenerys Stormborn Targaryen, is very far away and is not even close to making it back to regain the throne. By their law, she is the true heir to the throne. However, with Robert dead, it should fall to his heir. The big problem is, his children are not his...they are his brother in law's sons. Eddard Stark (and the kings hand before him) found this out, and for this they both died. The actual heir to the throne would be Stannis (he's the next oldest) or Renly (youngest). After that, it would be Gendry and any of the other illegitimate children that Robert has.