My son and his ex have a 21 month old daughter. All 3 have lived with me since the baby was 10 days old. Mom moved out for the 3rd time in Jan. and only comes around now when she wants something but uses the baby as an excuse to come. She does not provide any support at all. It is usually about 1 - 1 1/2 weeks between visits with no phone calls in between. We never really know when she will stop by. She usually calls, says she is coming, but does not show up. Is this considered abandonment? My son is listed on the birth certificate as father, what does he need to do to get custody?

It is not considered abandonment.

Your son needs to go to court and request custody. Since it appears he has primary custody already, its usually a slam dunk. The mother will then have to request visitation and she will be set up with a schedule.