This paper provides an answer to the question why birth parents have a moral right to keep and raise their biological babies. I start with a critical discussion of the parent-centred model of justifying parents’ rights, recently proposed by Harry Brighouse and Adam Swift. Their account successfully defends a fundamental moral right to parent in general but, because it does not provide an account of how individuals acquire the right to parent a particular baby, it is insufficient for addressing the question whether and why there is a right to parent one’s biological child. Such a right is important because, in its absence, fairness towards adequate prospective parents who are involuntarily childless would demand a ‘babies redistribution’; moreover, in societies with entrenched histories of injustice there may be reasons of fairness for shuffling babies amongst all recent parents. I supplement the Brighouse-Swift account of fundamental parental rights by an account of how adequate parents acquire the right to parent their biological babies. I advance two arguments to this conclusion: by the time of birth, the birth parents will have already shouldered various burdens in order to bring children into existence, and are likely to have formed an intimate relationship with the future baby. Denying birth parents who would make at least adequate parents the right to keep their baby would be unfair to them and would destroy already formed parent-baby relationships which, I assume, are intrinsically valuable.