Can grandparents dictate visitation for parents?

Here's the situation: young dating couple gets pregnant while living together. They move onto the girl's parent's place. They have the baby. Grandparents kick father out (when baby is approx 3 mos) because the couple is always fighting. A few weeks later, mom abandons baby and leaves it with her parents. Grandparents take control and dictate how and when the father can see the baby. The mother has never held down a job and did not finish high school. The father was sporadically employed but has recently started in a stable job. Neither parent has their own home but the father lives with his parents in a stable home. The mother is MIA. Where can I find out details about what rights the father and grandparents have in this situation? Can the father just keep the baby during one of the visits?