Is it true that a parent who has signed the birth certificate is automatically granted custody?

In Ohio, the rights of the father and the mother are established by ORC3109.042: *An unmarried female who gives birth to a child is the sole residential parent and legal custodian of the child until a court of competent jurisdiction issues an order designating another person as the residential parent and legal custodian.* ** If the father has not been to the court for an order of custody modification or visitation, AFTER establishing he is the father, then he has no custodial or visitation rights to the child. Please consult with an Ohio Domestic Relations attorney before proceeding in this case. The information published here is for entertainment purposes only and may not be taken as legal advice.

No. His signing means he is your biological father only. He would have to file to get custody.

Signing the birth certificate does not confer custody on a father in Ohio. An unmarried mother has full custody, and the father would have no rights to contact, visit or exercise custody over the child absent a court order granting him those rights. A conviction for child endangering, depending on the circumstances, may have a greater or lesser impact on custody and visitation rights. A court sentence directing that a person not be permitted to be around minors would not as a matter of law prevent a court from awarding custody to that person, but would very likely lead a court not to grant him custody, or probably even visitation. A person who was not with the mother when the child was conceived is probably not the biological father, which would likely further impact his ability to obtain any sort of parental rights.