There has been a recent trend of teens attempting to see if they could file a divorce from their parents. Children are not able to file a divorce because the splitting of a parent to child relationship does not fall under a marital agreement.
If a child for any reason does not want to be in the custody of a parent , they could have relinquish all rights to be your parents. This is not a form of divorcing but a parent relieving themselves of their parental role. If the house in which the child resides has become unstable, a social worker will need to be called in and this will also be a way a child can remove themselves of their parents custody.