When I die can I give custody to my child's step father or will the biological father gain full custody?

The Biological father is who would have the rights the courts would back being the other biological parent.

A child is not property that you can bequeath rights to. You can express a preference in your will but its not legally binding. As long as the bio father has parental rights he can claim custody for your child should something happen to you.

The child's step father can petition for a step parent adoption which would terminate the bio father's rights. But the bio father would have to agree unless there are legal reasons to terminate his rights.