Allegedly the better the stats of the parents at the time of birth (not becoming adult) the better the chance of a child with good stats.  But considering my sovereign is usually 5 str, 10 dex, 10 cha, and 15 int/ess/con and my wife is generally Rilis (can't remember her exact stats but they're high, like 18 str) and my children are almost always without fail 10 across the board I don't know.

Basically it's random except essence is apparently 50%-100% of the parent with the highest essence.

Also female children will (almost?) always have the abilities of the female parent and male children the abilities of the male parent.  Abilities like adventurer, ugly, etc...