You can bring a petition to terminate the rights of the natural father if you meet the criteria. Two years without any contact would be one factor in your favor, but there are others than must be considered. Terminating parental rights is not easy, and you will need an attorney as doing it yourself is nearly impossible. This is because parental rights have constitutional protection. I recommend you consult with an attorney in your area who is familiar with proceedings of this nature and has successfully prosecuted same.
Answered on Aug 19th, 2014 at 11:14 AM