Question about custody

So me and the father of my baby are not together, the baby will have my last name but he will still be on the birth certificate. He's a drug addict and if he doesn't get clean and go to rehab before the baby is born I don't want him to have any sort of visitation or custody of our baby. Is that possible?

His mom tries to convince me that the courts will do supervised visitation like they did with his dad (a meth addict) which is exactly what I don't want to happen because I don't want my son growing up like my ex did and become an addict from being around it