Hey there,
sorry for the AUC date error, don't know what i was thinking.
So the game starts 20 years after Alexander the Great's death.
I did not dig inside the in game familys and what choices have been made by the team BUT, from an historical point of view as i remember my antique and few reads :
The only heir with a strong claim, Alexander the 4th of Macedonia, son of Alexander the Great, was underaged and assassinated by Cassandre 13 years after his fathers death in 310 BC (wich is if i'm not mistaken, 7 years before the start of the game)
Even Alexander's illegitimate son, Heracles, is out of the game, being assassinated in 309 BC.
Non-mentioning the fate of Philip the 3rd, Alexander the Great's step brother, who was described as mentally ill anyways, assassinated in 317 BC.
So starting from there and contemplating the various political plots in the following decades (yeaaaaah princess, kings, satraps, military leaders, i'm speaking about all of your tricky moves, yeah !), one of the maybe reasonable answer would be to give some credit to the Historical Library by Diodorus Siculus, book XVII, where he tells that Alexander the Great's answered the legacy question on his death's bed by "May it be passed to the strongest".
Where such a story, written by a Roman historian of Julius Cesar period more than two centurys after Alexander's death serves directly the ambition of the Roman Empire, it figures well what was probably the situation around 300 BC and for the years to come. A total mess.
Then, pretty any family bound to Alexander the Great's family tree, Macedonia, or even sattraps successor and their own legacy can have a form of legitimacy claming to reform the Empire in Alexander's name.
The ptolemaic part in Egypt, the Peonian one, even the Seleucid one where is located Babylon. I would clearly struggle to determine wich one has more legitimacy than another.
