29 year old Nancy Gonzalez was a federal corrections officer when she was impregnated by death row inmate Ronell Wilson who has been convicted of murdering two police officers. Their son, Justus, is now seven months old is in the custody of one of Gonzalez’s relatives. Wilson request for parental rights has been denied since he is already "civilly dead". Gonzalez has lost custody of Justus since she intentionally became pregnant during the commission of a crime (having sex with a death row inmate while a correction’s officer), knowing that neither parent could care for the child.
Gonzalez also admitted to going through an "alcohol and cocaine binge" when she was eight months pregnant and to also driving while intoxicated with Justus in the car at least twice.
So it appears, at least in New York, death row inmates lose custodial rights to their children since they are considered "civilly dead".