The third and least significant contender for the throne is the powerbloc forming around and instigated by House Formorian. Lord Kaled (son of Balor, son of Belshazzar, son of Dios) has asked the College of Heralds to confirm him as King and has begun gathering what allies he can, which so far consist of House Olympus and the Free City of Sarantium, though the prospect of House Darios joining them once their civil war is settled seem good.
Formorian possesses no significant armies, no significant allies outside of Chaos, no powerful artifacts save for Olympus' Logrusfoil, Love, a legal claim so weak a child could likely defeat it in legal debate before the College, and no compelling political platform to inspire grass-roots support from the masses. Also, most other Chaosians find them creepy. It seems quite unlikely that Kaled will ascend to the Throne.
It should be noted, however, that while Kaled is generally regarded as crazy, one does not survive long as a Great Lord by being stupid as well, and that he perhaps knows more about his capabilities than we do.