Now, as the title implies, there are a variety of claimants. First, of course, we have Palpatine's niece, Ederlathh Pallopides. However, she's likely descended from Palpatine's father's mistress, as good old Sheev killed his siblings and mother. Anyway, she's a woman, and the Empire isn't big on them. Non-huMan after all. The next options would be the Emperor's only son, Triclops, and his grandson, Jedi Prince Ken. However, one's a crazy mutant, and the other is . . . well, he's Ken. Now, these assume that the Imperial Throne is based on blood inheritance. It could be argued that is based on the Baneite Sith line, with Apprentice following his slain master. In which case there are two real claimants for that honor. Lumiya's line (which seemed to be the one followed in canon, with Carnor Jax taking the title Emperor for a while) would be the first. The second would be Luke Skywalker, who, in Baneite tradition, fell to the Dark Side and selw his master in Dark Empire.