The court will consider what is in the best interests of the child (children) in determining custody. There are two types of custody; physical custody and legal custody.  Physical custody is the person with whom the children live.  Legal custody is the person who makes decisions about health, education, etc. Although it is not possible to predict the court's ruling, it is unlikely that the court would award physical custody to your ex-husband, who abandoned his children and whom his children don't even know.  The judge is not going to remove the children from your home and award physical custody to your ex-husband as this would not be in the best interests of the children and would be traumatic for the children to be separated from their mother.As for legal custody,  joint legal custody is a possibility.   This means that both you and your ex-husband would make decisions regarding education, health of the children, etc. Child support and custody are separate issues.