What is written on their birth certificates is false information provided by their mothers to cover the result of an affair. In one case, the genetic characteristics of the child are so different than those of either the mother or her husband, that it's amazing that the husband has never suspected anything. He looks just like his real father. I have also counseled and received letters from men who are devastated when they discover that their wives are pregnant with someone else's child, or discover after the child is born, that it is not his. And I have counseled and received letters from the lovers, who know the child is their's and are tormented by a desire to become involved in their child's life as it is growing up.
Pregnancies are very common in affairs.
The passion of an affair makes birth control less effective, and it's often never even used. And birth control is not all that effective even when it is used. I know of a couple that faithfully used two forms of birth control whenever they made love, and yet had five unplanned children. Most women who become pregnant from an affair have an abortion as soon as the pregnancy is discovered. But there are many who simply cannot let their child die that way.