The answers will obviously depend upon the facts you've not given, but the general answer is "yes, it is reasonable under certain circumstances." If he knows he's the father, is on the birth certificate, and especially if he requests contact with the child, then the court is not going to merely sweep him aside. The court will want to know why he has not had any contact with the child or why he hasn't provided any child support, assuming he hasn't. But if he is not on the birth certificate, and if he is claiming he is not the father, then the law automatically presumes that she has sole custody. This is a simplistic answer and doesn't discuss things like termination of parental rights or step parent adoptions (should you and your girlfriend marry). So my advice is for her to get in to see an attorney who can review all of the details with her and give her some good advice.
She has full legal custody if the child has been abandoned to her care and a court has not ruled otherwise. Eventually, if she otherwise qualifies, she may seek to terminate the father's parental rights. If the father is now taking her to court to establish custody, he will get some visitation, and be allowed over time to build that up and develop a relationship with the child. There are no short cuts to sitting down with an attorney for a consultation to go over your specific facts and circumstances to determine how to best proceed legally.
Responses are for general information purposes only, and are based on the extremely limited facts given. A consultation with an attorney experienced in the area of law(s) indicated in the question is highly recommended. Information and advice given here should not be relied upon for any final action or decision, as the information is limited by its nature to the question asked and the fact(s) presented in that question. THIS RESPONSE DOES NOT CREATE AN ATTORNEY/CLIENT RELATIONSHIP, particularly considering that the names of the parties are unknown.
Since the father has been absent for at least 2 years, it is very likely that mom would receive custody of the child. Most, if not all, of the judges will allow for the father to establish a relationship with the child if the father is serious about wanting a relationship with the child. This would happen gradually over time with the father receiving more time with the child as the relationship builds.
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