I have a son who is getting ready to turn 3 in October, his father has only seen him I would say around 10 to 15 times for only short times and the last time he has seen him was January of 2007, but he did pay child support for the following months oct 2006, nov 2006, dec 2006 and then August 2007-dec 2007 and then Jan 2008- May 2008, but he is still behind 1800. And I waived the first year of child support so that he could start with a clean slate in Oct. 2006. What I want to know is since he has made no attempt to really see his son and is sporadic at paying child support. Could I possible take him to court and file abandonment papers, because I don't want him to just think that sometime in the future he could just show back up, I have no clue where he is living or if he is even in this state. What should I do? Do I have a case for abandonment, or could I petition the court to have him sign up his parental rights.

Go to court and get them to try and reinforce the child support. They are suppose to be able to track down dead beat dads. Then IF he does reappear in your kids life and want to be a part of it tell him to go to court for visitation rights and he will have to follow them or forget it.
You can't 'get him for abandonment' or signing away his rights though

Child abandonment involves leaving a child without ANYONE to care for them. So what you are really asking here is can you terminate the father's parental rights (TPR). You may be able to use abandonment as a grounds for obtaining a TPR. But it's a longshot. Generally TPRs are granted only to clear the way for an adoption or if the parent represents a danger to the child. Neither seem the case here.

I can understand your not wanting the father to think he can just waltz back into the child's life. I would petititon the court to remove his visitation rights and force him to go to court to get them reinstated. Biut I would forget a TPR.

I have a son who is getting ready to turn 3 in October... Do I have a case for abandonment, or could I petition the court to have him sign up his parental rights.
My hunch is that if you marry and your husband wants to adopt your son, then you can request the court to terminate dad's parental rights. Until then, sic the gov't on him and ride him like a pony. Do you have his SSN?