A petition/lawsuit must be filed in Circuit Court requesting that the court to grant you custody of your child(ren). If both parties agree and sign an agreement (called a Consent Agreement), that will be entered as a custody order (if the Judge approves the terms, too).
As mentioned, if paternity is established through an Affidavit of Parentage, the legal father does not gain enforceable legal or physical custody of the child. By Michigan statute, the mother keeps full legal and physical custody of her child until a court order changes this status. Often, the Acknowledged Father benefit from the formality of a child support order because his right to legal or physical custody will be addressed, and a court order giving him some level of physical or legal custody is more than he had through his acknowledgment of paternity form.