The Theory of Parental Responsibility holds that parents have enforceable positive obligations to their children because people are responsible for the consequences of their actions. Given that parental obligation only arises as a consequence of action, there are cases in which a child can come into existence without a parent incurring positive obligations. This article explores when this applies and when it does not apply.
Unintended Parenthood
Obligation obviously applies in all cases of intentional parenthood, but obligation also applies to unintentional parenthood. This is the same as with other unintended consequences of actions. If a careless car driver hits a pedestrian, the fact that he did not intend to harm anyone does not remove his responsibility. The same logic applies to parents who did not intend to have a child. If you take actions that could result in the existence of a child (i.e have consensual sex) then you are responsible for the child, even if you didn't intend it or want it. As Nathaniel Branden put it;
The fact that the parents might not have desired the child, in a given case, is irrelevant in this context; he is nevertheless the consequence of their chosen actions–a consequence that, as a possibility, was foreseeable.
Adoption
I have argued elsewhere that adoption also appears to entail parental positive obligations, although I am not certain of this.
Rape
In a case of rape, the rape victim would not have parental obligations since the victim did not take action that results in a child being created. It was the rapist who acted, and thereby forced those consequences on her.
The rapist would have obligations to support the child, although a reasonable legal system would presumably deem him a criminally unfit parent and deny him access, so his obligations would have to be in the form of monetary payments to whoever was the caregiver of the child for the child's support, alongside restitution payments to the victim.
As a side note, the fact that there are no positive obligations in cases of rape victims means that parental obligations do not provide an argument against abortion in those cases. In cases of consensual sex, parental positive obligations do refute the right to abortion, but not in cases of rape. Whether or not abortion is justified in those cases depends on other arguments.
Artificial Circumstances
There could be other situations in which natural parents would not have positive obligations, such as by contract. In cases such as where a man donated sperm, or a woman donated an egg, or a woman acted as a surrogate, none would have positive obligations (assuming there was a contract which designated alternate adoptive parents).
If a man's sperm or a woman's eggs were stolen from a storage facility, neither biological parent would have parental obligations since they would also not be responsible for creating the child. The thieves who created a baby using the sperm or egg would have parental obligations, but like the rapist they would be criminal and may be found unfit to act as parents, depending on the circumstances.