There has been long-running debate about the proper standards for how biobanks might secure ethically sound acquisition, storage and research use of human biological samples and personal data derived from them. Part of this broader debate has focused on the kind of consent framework that is morally required. Some argue that informed consent must be secured on a case by case basis. . However, the scale, heterogeneity, and long-term nature, of biobank research gaining project-specific consent is apt to be costly, administratively burdensome, and problematic. Others argue that some kind of broad consent to types of use, and user, and frameworks of governance is sufficient. Here the aim is to critically assess a line of objection that, if sound, does not depend upon the question whether broad consent is informed consent. The objection is a substantive one in its own right: that broad consent frameworks fail to respect or properly accommodate the participants ongoing right to control access to and use of her samples and personal data. We clarify what a right to control is, showing how this kind of right to control is grounded in more fundamental moral rights. However, by attending to the social context of seeking and giving permission it is then shown, perhaps surprisingly, that although participants do have this moral right to control, broad consent frameworks do not infringe, breach or fail to respect such a right.