My son has been taking care of his 2 kids everyday since May of 2010 before that on and off he lives in Houston she lives in Corpus. The time she did have them she would call in a week that he needed to come pick them up and we would. Finally in May she threatened to call CPS and give them up for adoption if we could not keep them. My son has had since, my question is wants to file for custody but we knows she will try to hold on too then since they are her bread and butter she lives in a 3bedroom government housing and receives food stamps she also, files false claims or allows someone else to claim every year in order to get the earned income. He loves his babies and says he will never let her take them but, I know that any given time she can show up with the cops and claim her kids. The baby is only 15months and does not know her and his son is 3yrs and will be devastated if he is taken from his daddy...

First, abandonment doesn't apply here. Abandonment is a criminal charge for leaving children without adult supervision.

Before we can truly help, we need to know more about the situation.

Was he ever married to the mother?
Is he on the birth certificates or signed acknowledgment of paternity?
Has there been ANY court action ordering custody, support or visitation?
Is he paying support? If so, voluntarily or through a state agency?

If he can prove that the children have been living with him SOLELY for more than 6 months, then there may be a good chance for getting primary physical custody. If the mother has been collecting public assistance based on being the primary caregiver when she is not, she could be facing criminal charges.