Originally Posted by TinCow
In my experience the size of your family is directly related to the size of your empire. The more you expand, the more your family expands, either through births or adoptions. You will notice a distinct lack of births when you have stabilized your territory for a long period of time. If you then take several provinces quickly, you will receive a large number of births.
Adoptions and Man of the Hour seem to only happen when you are far below the number of family members that the game thinks you should have with your empire. As such, if you really want to try and manufacture a Christian child, you should continually kill off pagan family members to keep your birth rate up.