Modern biomedical research into the genetic component of common diseases calls for broad access to existing and novel collections of samples of human biological material, aka Biobanks. Groups of donors of these samples, however, increasingly claim a property right in their samples. They perceive the recognition of a personal property right in their biological material as the best means to serve two goals: to secure ongoing control over their samples after donation and to underpin their claim for a share in the proceeds that the research on their samples may yield. Given the objective of ensuring ongoing control, this property right is claimed to be inalienable. Recognition of a personal property right in one s biological material is problematic, especially where the requirement of inalienability seems at odds with the claim for a share of the profits. Yet, property rights in human biological material may be justified in a certain context, e.g. to enable subsets of patients to negotiate the terms and conditions of the research into their specific disorders. Biobanks, however, contain so many samples, which can be used for so many research purposes, that the unrestricted exercise of personal property rights by the sample donors will lead to a proliferation of rights. This proliferation is likely to deter or slow down both the creation of de novo Biobanks and the use of existing sample collections. Thus, recognising inalienable property rights in human biological material may lead to suboptimal use of these resources and create a classic anticommons property scenario. It would also undermine the current trend to simplify existing informed consent requirements which aims to facilitate broad and previously unanticipated research on de novo and existing Biobanks. In addition, the tradition of altruistic participation in research and the notion that large-scale collections of human biological material are global public goods are arguments against recognising inalienable personal property rights in human biological material, at least in the context of Biobanks. To avoid uncertainty over the issue of who owns collected human biological material, the principle that the property rights in such material vest in the entity lawfully collecting and storing the material should be implemented in legislation. This way most individuals and their offspring will benefit more than when they heed the call to stand up for their property rights in their samples.