Biological father died mother has surgery but dies on the table what are the rights of the step father in the state of Ohio?

Minimal. A lot would depend on how long he has been a step father and whether there are blood relatives looking to care for the children.

I agree with Scott, depending on the laws in Ohio (I am not an Ohio attorney). Generally, if the step parent can show that he is a "de facto" parent, meaning he has stood in the shoes of a parent and for all intents and purposes is the parent of the child, he could persuade a court to award custody to him, as it would be in the best interests of the child to do so. However, if the step father has been absent and say a grandparent or aunt has raised the child... they would be the best choice (barring any neglect/abuse).

Additionally, the age of the child will likely play a role if the child is of sufficient age to assist the court in making a determination of what's in his/her best interest.

Best of luck!