Yours. Doesn't really matter in my opinion if the Dad is going to be involved or not as you will be the one filling out the forms, having them on your medicare card, dealing with the school etc which to me, the practicality of it all is more important than either parent getting 'branding rights'.
My DD1 has her Dad's, it is a huge pain and something I regret. We are actually looking at getting it changed now before she starts school and her Dad agrees that it makes more sense for her to have mine. Currently myself and DP are her 'everyday' parents and it is just inconvenient that she doesn't share either of our name so 3 surnames in the household. DD1 stays with her Dad for a night a week, he is actively involved but in the end, most times when a surname is required, DP and I will be the ones standing next to her. I think a 'present' Dad is even more likely to see the benefit in giving them yours because they will want what is best and easiest for their child, at least that is the case with DD1s Dad (in that he is even comfortable with her having DPs surname which I really respect about him -- he knows being her Dad is more than a name and just wants what is best for her).
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