I am the child's relative. Can I get custody of the child?
A non-parent can ask to be appointed as a legal guardian if the child is being neglected. The court must find that it is in the best interest of the child that he/she should have a guardian appointed.1 Being legal guardian is similar to having custody, but is not exactly the same thing since the parents still have some rights and responsibilities for the child.
A blood relative, foster parent or parent may also request permanent guardianship over a child in certain situations.2 This is more like establishing custody, but is legally different.
"Custody" in Delaware is for parents. Parents include birth parents, adoptive parents, and "de facto" parents, which means any person who has acted like a parent to the child, with the consent of the child's actual parents.3
1 13 Del. C. § 2330
2 13 Del. C. § 2353
3 13 Del. C. § 8-201