He can certainly sign a statutory declaration to this effect, the real question is whether or not it has any legal weight.
The answer then depends on what you want. Do you want him to do that because you want him out of their lives and have a step-dad in mind, or do you still want him to pay child support and make joint decisions on their upbringing?
I'm not 100% of the answer and will leave the more experienced family law experts to comment.