Broad consent is increasingly recommended as an acceptable consent model for biobanking human samples and health data with a view to their future use in research. Empirical evidence on the practice of broad consent and its implementation in the hospital setting, however, is still very limited. We analyse and discuss results from a qualitative study of perceptions of a sample of patients and biobank recruiters regarding broad consent to participate in a hospital-based biobank for prospective research on genomic and health data. Our findings suggest that contextual and relational factors play an important role in the practice of broad consent, and illustrate that broad consent relies as much on intuition as on reasoning. Moreover, we show that seeking broad consent in the hospital affects patient-recruiter interaction and that "conditional" trust plays a significant role in broad-consent decision-making. In conclusion, we provide recommendations to improve patient autonomy in the context of hospital-based broad consent.