Because these births are part of a secret society, we will not know the exact number. Recently, the Boston Globe ran a two part series about children whose fathers are priests. It included many interviews with these children in adulthood. They lived complicated and often unhappy lives carrying with them a secret and often feelings of guilt.
We all know there are gazillions of babies born from secret sexual relationships and many of these children will have problems dealing with their circumstances. Children of priests have an even bigger hill to climb because their own religious devotion to the church is sometimes involved and the confusion that entails.
So far, the Catholic Church has refused to take any responsibility for these children. Priests seldom provide financial support. Some interviewees had priest fathers who played a role in their lives and were instructed to refer to the priest as “uncle”, not “dad”.
The Church’s rules on priest celibacy was not the only problem. When the mother was married, as was the case with one interviewed man, the divorce taboo was so powerful the children had to be reared by a mother and an angry husband who knew the priest who had fathered the child. The child looked like the priest and the probably the husband was reminded of his wife’s infidelity every day.
The Catholic Church should recognize this is a permanent problem. There always have been and always will be children of “celibate” priests.
The solution, eliminate celibacy and the divorce/remarry taboo. Join the human community.