Hypothetical question

So this is super random and kinda dark, but I’m curious if anyone has any guesses to this question..

I have a 9 month old, his dad is not around, but does pay child support. He’s on the birth certificate only because in the state of Ohio once paternity is established they automatically put them on, but he was not originally.

In the state of Ohio full custody goes to the mother unless otherwise agreed upon in court. Child support and custody are two separate courts, so we have no state mandated custody/visitation.

If I were to die, who would my son go to? Would he be put in the care of the state until something is worked out? Would he go to his dad?

Needless to say, this thought made me go “oh shit!” And I will be working on a will... but god forbid anything ever happened it made me curious.