I have recently been granted sole legal and physical custody of my children, ages 12 and 14 in the state of Maryland. They ( the children) had a lawyer appointed the case. The court said it was in the "best interest of the children". The father has not shown any interest in seeing them, and has an arrears amount in excess of $12000. The children have expressed an interest in having my husband adopting them and changing their last name. Their biological father is currently on parole for a violent crime against his ex. My question is, do I need his permission?

Yes, your ex will still need to revoke his parental rights in order for adoption to take place.

I'm going to slightly disagree with J_9 here. You don't absolutely need to get the father's permission. But you do need to try. Given the circumstances, if he refuses, it is probable the court will grant the adoption over his objections. The father needs to be served notice of the adoption petition and be given the chance to object.

I would not attempt the adoption without an attorney under these circumstances.