Custody of a non-marital child upon the death of the mother

Dear PAO,

My sister died, and she was survived by my 5-year-old nephew. My sister and my nephew's father were never married. Upon learning of the death of my sister, the father signified his plan to take over the custody of my nephew from our parents — the maternal grandparents. The father argued that as a surviving parent, he has a better right over the maternal grandparents of a non-marital child. Is this correct?