Complex sentence: The immense power of living emperors, on the other hand, was mediated through the encompassing agency of the state: once acknowledged as "paterfamilias" to an Empire, the princeps was entitled to "genius" cult from Imperial subjects of all classes.
Split into simpler sentences: The immense power of living emperors, on the other hand, was mediated through the encompassing agency of the state. Once acknowledged as "paterfamilias" to an Empire, a princeps was naturally entitled to "genius" cult from Imperial subjects of all classes.