The biological father of my child had made it abundantly clear that, when I decided to keep this child, against his wishes, I would be taking care of the child myself as he wants no part in this child's life. Falling pregnant was not planned and came at a time in his life where he felt unable to support, raise or in any way be part of another baby's life as he already had a young baby from his ex-partner.
We verbally agreed that no support, monetary or otherwise would be expected from him, basically totally cutting him out of the picture; he is happy with that, I am happy with that and we have since dissolved our relationship and have had no communication.
However, I now feel that I need more security regarding the above.
I feel that my baby's life can do without being tainted by his history of irresponsibility and would like to make our verbal agreement legal and binding.
Would a written and signed contract between us, stating his voluntary termination of his paternal rights, be legal and binding?

If you would have read the stickie at the top of the page, searched the 1000's of similar question you would have seen

1. verbal agreements have no bearing
2. written agreements unless signed by the judge have no legal weight, while shows intent, can not be inforced

Almost never will the courts merely take away a fathers rights, unless the mother is remarried and the new husband wants to adopt

You can not take away his requirement to pay support, while you may not try to collect, if you or the child at anytime receives any state or government assistance, the state will go after him for repayment, esp if he is not paying child support.

Next you are morally cheating your child out of the money the child is due for help in the raising and support.

What you do, is get a court order for sole custody both legal and physical, then the man does not ask for any visits. There will be a order for child support which is normal and should be done.

I just have to echo what fr_chuck stated. Please put him on support even if you never see a dime. In my state they are doing the every 3 month round up of arresting all parents who are not paying support and the other parent is receiving medicaid, food stamps and so forth.

First, where are you located? The term "falling pregnant" indicates you are outside the US. Laws vary by locality. I don't understand why someone would ask a legal question without giving a general location. Also, for future reference as Chuck mentioned, there are sticky notes at the top of many forums that answer frequently asked questions, or provide guidelines for using this site. You can save yourself time by reading them.

I would suggest consulting a local Family Law attorney. They can tell you what local laws apply. If you want to proceed with this you will need one to file the paperwork.

Thanks all for your input - I live in South Africa and am South African while the father is French. It seems this is a U.S specific site so will seek advice elsewhere.