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Cross-shelf transport plays an important role in the heat, salt, and nutrient budgets of the continental shelf. In this study, we quantify cross-shelf volume transport and explore its dynamics within a high-resolution (2.5–6 km) regional ocean model of the East Australian Current (EAC) System, a western boundary current with a high level of mesoscale eddy activity. We find that the largest time-mean cross-shelf flows (>4 Sv per 100 km; 1 Sv ≡ 106 m3 s−1) occur inshore of the coherent western boundary current, between 26° and 30°S, while the strongest time-varying flows occur in the EAC southern extension, poleward of 32°S, associated with mesoscale eddies. Using a novel diagnostic equation derived from the momentum budget we show that the cross-shelf transport is dominated by the baroclinic and geostrophic component of the velocities, as the EAC jet is relatively free to flow over the variable shelfbreak topography. However, topographic interactions are also important and act through the bottom pressure torque term as a secondary driver of cross-shelf transport. The importance of topographic interaction also increases in shallower water inshore of the coherent jet. Downstream of separation, cross-shelf transport is more time-varying and associated with the interaction of mesoscale eddies with the shelf. The identification of the change in nature and drivers of cross-shelf transport in eddy versus jet dominated regimes may be applicable to understanding cross-shelf transport dynamics in other boundary current systems. Significance Statement Cross-shelf transport, i.e., the movement of water from the open ocean on or off the continental shelf, is not reported often as it is difficult to measure and model. We demonstrate a simple but effective method to do this and, using an ocean model, apply it to the East Australian Current System and show what drives it. The results show two distinct regimes, which differ depending on which part of the current system you are in. Our results help to place observations of cross-shelf transport in better context and provide a framework within which to consider the transport of other things such as heat and carbon from the open ocean to the continental shelf.