I just found this:
Definition:
Abandonment refers a parent's choice to willfully withhold physical, emotional, and financial support from a minor child. In other words, abandonment is when a non-custodial parent fails to fulfill his or her parental responsibilities and chooses not to have contact with his or her child.

Abandonment can result in the loss of one's parental rights. However, a parent cannot simply choose or elect on his or her own to forfeit those rights. In fact, even in cases of abandonment, most states will not legally terminate a parent's unless there is another parent-figure, such as a step-parent, who is waiting to formally adopt the child.

Legally, in most states, a parent is said to have "abandoned" a child after a two-year period of withholding his or her contact and financial support.

I would say talk to a lawyer or DCFS and see what your state laws are...

What do you want to happen?