Apparently you have to marry someone to have a child. Just like real life! (oh wait..) You can have up to four children and that is it, because, well, I don't really know.
That said, you can never remarry and never have bastard children. Why? Because... I don't know.
Seems it would open a lot of ground, much of it historical, if you had bastard children, annulments, etc. Perhaps a factor of your wisdom in regards to bastard children? If you are wise, you know this could cause problems with your dynasty and perhaps have it tied to the wife. Obviously, if the queen is pregnant, she has a pretty solid idea of who the father is, unless she is on Maury "Who's the daddy" show. He has to take her word for it and that brought up many a device for preventing it and jokes for it.
There are several elements here that are not being explored yet. While controversial perhaps, they are part of the fabric of the genera.