So assuming that I have not harmed my child by fathering it, nor do I owe the mother any further compensation assuming that the contract was paid as negotiated, how would a father become 'responsible' for a child without declaring that responsibility for himself (in an ancap society, for consistancy)?
Well, the simple answer is that you can't. Of course, there's a much more complex answer, and that involves the fact that without claiming responsibility for the child, you can't claim parental privileges to it, either. If you wish to take any part in the rearing of the child, you must take responsibility to do so. In other words, if it's your child, you are responsible for it. If you wish to not be responsible for it, it's not your child.
If he has caused no harm, nor accepts the responsibility upon himself, who/what can impose that responsibility upon him?
As I said above, only his desire to take a hand in raising the child. It's a privilege/responsibility "package deal." It can be argued that since a child is a financial liability (a fact which I quite well understand), a father has financially burdened the mother, and should pay recompense.
Of course, in modern society, the mother is not required to keep the child, or even bring it to term. She can abort the pregnancy prior to 25 weeks, or place the child up for adoption after birth. So a single mother really, only has herself to "blame" for the financial burden, and she can always seek another person to help provide for the child. Again, in today's society many men, or even women, are willing to accept responsibility and care for another's biological child. (The father, should he find himself single, of course has this option as well.)
Now, to be clear, I do agree that any parent has a difficult to define responsibility to his/her children; regardless of the conditions that resulted in that child. I'm just trying to guide you to the source of that responsibility.
I don't think it's hard to define, or determine where the responsibility comes from. Your responsibility is to raise the child so that it will not cause harm to itself or others, and the source of that responsibility is that it is
your child. You made it, you have to see that it is raised properly, for it's own sake. (Ultimately, the source of the responsibility is the child itself.)
Now, as I said earlier, responsibilities can be delegated, in this case either by hiring a nanny/baby sitter/etc, and making sure that they are teaching your child correctly, or you can give up the responsibilities and privileges by handing the child off to an adoption agency or other form of child care.
The father can delegate this responsibility entirely to the mother (as you did in your example) but unless the father is unaware (or, as in the case of your example, has already relinquished any privileges/responsibilities as part of the original hire contract), this is seen as socially unacceptable. A "dick move," if you will. If he sticks around, however, he has accepted that responsibility, and if he wishes to delegate it later, it must be done somewhat more formally.
The mother, if she chooses to carry the child to term, has accepted that responsibility, and must then carry it out, either by raising the child herself, or delegating the responsibility in one of the above fashions. (Perhaps, even, completely to the father, if he stuck around, and she does not wish to - I'm sad to say my sister took this option not once, but twice. It's no less of a "dick move" when the mother does it.)
Assuming the prostitute keeps the child, which is decidedly not a given, you have incurred no responsibility, since when you left to go home, you left the decision entirely in her hands. She, however, has incurred a responsibility to raise the child. Do you dispute that?
Actually, I do. This is a contradictory position, but we will get into that later.
Which part do you dispute, that the mother has incurred responsibility, or that the father has not?