Well, I think you have a lot plopped in your lap, but let's back up a bit...
.... first of all, you are NOT a stepmom yet. You are in a long distance relationship with a man who may soon have custody of his daughter. I say that not to diminish your feelings, but to put it in perspective.
This would be a great thing to take to a counselor, advisor or mentor. There are always challenges with long-distance relationships, add to it that you and he will still be learning about how to live with each other day in and day out. That, in itself, would require support. If you have plans for a future together, married or not, I would strongly suggest some couples or premarital counseling. This really helps couples to start their new lives together with a stronger foundation than they might otherwise. This will also give you an ability to learn more about him, his values, and for him to learn about yours. What are the hopes and fears you have in common and independently?
I also suggest this sort of support because blending families (even being a step-parent) can be very difficult initially. I say this as a stepdaughter four times over.... This girl of his is either going to be very hurt that her world is changing and mom 'doesn't want her'... and frankly, I'm going to be blunt here-- if *he* had been hankering to see her, he could have made more of an effort, taken her to court for more visitation. (I know, I have a father who was like this, content to let other people make choices for him-- it hurts as the kid, who feels there should be no excuse if you want to see them that badly.-- This isn't said to be mean, but as a reality check that this kid has not been actively validated in real ways.)
So this little girl has already had some huge burdens placed on her. If you were my girlfriend in this situation, I would tell you to proceed with great caution. Remember, too, that while things are great right now and that you have plans with your fellow, that if something bad happens in the relationship and you have kids, this is how you might expect him to behave. The fact that you say the mom 'as it looks right now she s tired of that girl and wants him to take care of it.' -- makes me think that you are pretty fuzzy on the relationship in that area, it makes the child sound like a problem.
There's nothing wrong with not wanting to walk down that path. It doesn't make you a bad person. But be very, extremely wary of trying to connect where you might not have intention to stay.... this girl doesn't need any more disappointments. So back to my original suggestion-- get some counsel and decide what you really want, if you are 100% committed to the challenge of raising a very hurt adolescent. In a perfect world, this would be a wonderful experience for everyone involved-- but you do want to know what you are getting into. Doing some counseling for yourself and maybe even some Skype counseling sessions if need be with your boyfriend would be the first step before jumping into any sort of parenting role.
I hope things work out, no matter what you choose. I personally would walk away from something like this, but that's due to my temperament and personality. Only you can be the person to decide for yourself.
