Our office has maintained a family law practice in Alameda, Santa Clara and Contra Costa County for the past 31 years. I have represented several thousand of individuals in family law matters.
I wish I could give you a simple answer, but I don't believe one exists. Unless your ex is no longer alive, I believe this will be troublesome. If he has provided no support nor any contact with the child for over a year, there are the provisions in the law which allow you to petition the court to terminate his parental rights. With some exception, by and large the courts are only inclined to do this if there is also a contemporaneous Petition for adoption of the child filed by another competent adult. In most instances, this would be if you had a new husband. Although, with his total abandonment of the child, it is not impossible that other individuals could adopt the child when your ex's parental rights were terminated.
I hope this is helpful.
John N. Kitta