This natural‐scale experimental study combines structural modelling of soft‐linked normal‐fault relays with a CFD (computational fluid dynamics) numerical simulation of a range of unconfined turbidity currents overrunning the relay‐system topography. The flow, released from an upslope inlet gate 2000‐m wide and 50‐m to 100‐m high, rapidly expands and adjusts its thickness, velocity and sediment load to the substrate slope of 1.5°. A lower initial sediment concentration or smaller thickness renders the quasi‐steady flow slower and its sediment‐transport capacity lower. A 3D pattern of large interfering Kelvin‐Helmholtz waves causes fluctuations of the local flow velocity magnitude and sediment concentration. Four zones of preferential sediment deposition are recognized: a near‐gate zone of abrupt flow expansion and self‐regulation; a flow‐transverse zone on the counter‐slope of fault footwall edges; a flow‐transverse zone at the fault‐scarp toes and a similar transverse zone near the crest of the hanging wall counter‐slopes. The sand deposited on the counter‐slope tends to be re‐entrained and fed back to the current by a secondary reverse underflow. The spatial extent and sediment accumulation capacity of depozones depend upon the released current volume. The impact of relay system on an overrunning current depends upon the fault separation distance and stage of tectonic evolution. An early‐stage relay system, with small vertical displacement and little overlap of faults, is bypassed by the current with minimum flow disturbance and no pronounced deposition. An advanced‐stage system, with greater fault displacement and overlap, gives a similar hydraulic effect as a single fault segment if the fault separation is small. If the separation is relatively large, the flow tends to be internally redirected sideways from the ramp into the hanging wall synclinal depressions. Since normal‐fault relays are common features in extensional basins, the study bears important implications for turbiditic slope‐fan models and for the spatial sand prediction in subsurface exploration of faulted submarine slopes.