what happens if someone claims my child on their tax returns?

My SO's father told us "I haven't paid my taxes so I'm going to claim her." She is our 9 month old baby girl. How much money do you think he will get and will he be able to claim her every year then?? How will we be able to take him off if we want to claim her? 
EDIT: we take care of her. He has bought diapers and wipes since she was born (my boyfriend and I were finishing highschool), my BF and I bought all of her gear and everything else ourselves. My grandma buys her forumla sometimes. My boyfriend is started his job at the end of this month so he won't have to pay for anything. I just don't know how any of this works and don't know if it's a good idea or not.

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