Stars give a bonus in defense and morale only to soldiers near to the general AFAIK but are hugely overpowered in autocalculated battles, so you are often forced to fight on the battlefield if you don't want your Thorakitai Agemata Basilikou to be slaughtered by a bunch of peasants led by a 10 star AI general.
EB team gave AI generals lots of stars to grant them superiority against the player at least in auto-resolved fights.
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