I have a 10 year old and an 8 year old from a previous relationship. I lived in Indiana up until about 4 years ago - I moved to GA. I have been married for 7 years to a man who in that 7 years has raised my children like his own. Prior to moving to GA my child's biological father saw the 2 children every other weekend as ordered in the child support and visitation. He saw them about 3 more times in the year following my move. Child support was paid during that time as well. In the past 3 years child support has been very sporadic... I received it at one time from unemployment checks (about 6 payments) and then when the system caught up with him for about another 5 checks (this was a few months ago.) Then he mysteriously quit that job... The last time that the kids saw him was over 2 years ago. The last time that they spoke to him on the phone was April 28, 2007... and he promised that he would call again and never did. Now the holidays are approaching and he has called (I did not answer) I want to know what are my rights as far as his abandonment. Him not calling, not seeing them and lack of support as I understand it is abandonment! Am I obligated to let him just pick up in their lives again and call just this once and not anymore? I am always the one that is left picking up the pieces of their broken hearts after he makes promises. It hurts them and me I would love to just be done with the situation... I would love for my husband to adopt the girls but I don't think that the father would go for that - just to be spiteful! Can I get the courts to push it through anyway - since he has abandoned them? Is there a do it yourself way to fill out adoption forms... as I do not have the money required to go through with the adoption?

By law he hasn't abandoned the children. He is making child support payments (regardless of how they come, or if they are sporadic). You stated that just a few months ago he was still paying.
Also it was your choice to move states thus obviously making visitation harder for him. I am curious, since you state there was a visitation order, did he consent to you moving with the children? If not, he very well could take you to court over that because you are hindering his visitation rights.
But in regards to that, he has not abandoned them in that sense either. You just said he called recently but you chose not to answer. You can't say he abandoned the children when you are preventing him from talking to them.

In Ohio it is a min. of 6 months with no child support and no contact before you would have grounds for abandonment. But abandonment gets you no where unless you are trying to have the children adopt... which will NOT happen unless the father consents to willingly relinquish his parental rights.

If you have read some of the other threads on this issue, there is no such thing as a charge of child abandonment unless the child is just left without any care. Abandonment MAY be used as grounds for a termination of parental rights, but is not a charge in itself.

If you want your husband to adopt, file the adoption petititon. You will need to get the bio father to relinquish his rightsor to involuntarily terminate them. The odds of either are not good, though he mght relinquish if he understands that relieves hi obligation to pay support.

You will need an attorey to file the adoption papers. That attorney can advise on the various methods to terminate rights.