Del. Code tit. 13 § 733
Notwithstanding that there is a surviving natural parent, upon the death or disability of the custodial or primary placement parent, the Court, at the request of the stepparent shall continue the placement of the child or children with the stepparent pending a hearing on the merits, provided the child has or children have resided with the stepparent immediately prior to the death or disability of the custodial or primary placement parent. Where the child has or children have so resided with the stepparent the Court shall apply the provisions of § 722 of this title and may grant permanent custody or primary physical placement to the stepparent. If the Court grants custody or primary placement of the child or children to the stepparent, the stepparent shall have all of the rights and obligations of a parent until such time as the stepparent no longer has custody or primary placement of the child or children.
13 Del. C. § 733