Quote Originally Posted by Martok
It's partially randomized, with the faction leader's high stats merely improving the odds of what his sons' stats will be.
With the most important stat being influence here. You can get an astonishing heir out of a mediocre monarch who has 9 influence; the other way round the same may happen and you get a worthless bugger from a king with awesome stats but 2 or 3 influence.

There seems to be a limit, though. Even kings with deplorable stats between 0-2 (including influence) won't get heirs which have even lower stats , i.e. closer to 0 on average - exceptions permitted of course.

I second Caravel in that 9 command remains 9 with an active general. Bestow command-boosting titles upon him or let him gain nice virtues - he never won't have more than 9 stars. The only case where a wraparound takes place are heirs to an already skilled, high-influence monarch. .... Never tried what kind of heirs such a 'wrapped around' king does produce, though, given that his own unit has a valour bonus of 5 for 10 command stars.

Btw speaking of command: Does anybody know how exactly the system works when the progress to the next command level is interrupted? E.g. if I need 128 victories to gain an 8th star and after 20 or so I lose a battle (and a star, accordingly), do I have to do the whole 64 victories to attain the 7th star again? Or are the 20 already won counted in?