I would argue that there WERE no legitimate heirs to Alexander's empire. Alexander was a truly unique personality, with enough tactical skill to continuously defeat larger armies, enough foresight to integrate his Persian conquests as much as possible, and enough charisma to convince his soldiers to follow him thousands of miles from their homes into hostile lands. Perhaps if he had lived onger he might have found some way to make a peaceful transition, but as soon as Alexander died his empire died with him, as none of his generals came even close to having the same persona as he did.