The closure problem of representing hydrological boundary fluxes given the state of the system has been described as the scientific ‘Holy Grail’ of hydrology. This relationship between storage state and flux should be hysteretic and scale dependent because of the differences between velocities and celerities in a hydrological system—effectively velocities are storage controlled, and celerities are controlled by storage deficits. To improve our understanding of the nature of these relationships a new hydrology model is used (the Multiple Interacting Pathways or MIPs model) to explore the influence of catchment scale on storage–flow–transport relationships, and their non-linearities. The MIPs model has been shown to produce acceptable simulations of both flow and tracer, i.e. of both celerities and velocities, at the Gårdsjön catchment in Sweden. In this study the model is used to simulate scaled versions of the Gårdsjön catchment to allow us for the first time to investigate the influence of scale on the non-linearities in storage–flow–transport relationships, and help us steer the quest for the scientific hydrological ‘Holy Grail’. The simulations reveal the influence of scale on flow response in the nature of storage–discharge hysteresis and its links with antecedent storage; fractal-like systematic change of mean output travel times with scale; the effect of scale on input, output and storage residence time distributions; hysteric relations between storage and output travel times and links between storage and water table level hysteresis.