Quote Originally Posted by I of the Storm
It's been a while since I played the Byz in MTW, but IIRC the first three or four princes always had high ratings in all fields + good V&Vs. They might be scripted. Not sure though...
Yeah, the general consensus is that they're scripted. Byzantine heirs are simply too good on too consistent a basis to *not* be hard-coded in some way, especially in the Early period.

As a general rule, however, what everyone else has said applies: Your heirs' stats are primarily affected by stats of your faction leader, with Influence being by far the biggest factor.