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Deep‐water sedimentation on active margins often entails complex sediment transport pathways through slope accommodation. Sedimentation in such settings is commonly differentiated into 'fill and spill' vs. 'tortuous corridor' models. To investigate the utility of these models in convergent settings 15,344 km2 of 3D seismic data is used to investigate sedimentation and erosion patterns across the Hikurangi subduction margin. A series of thrust‐bound trench‐slope basins, each tens of kilometres long by kilometres wide, have been diachronously forming, filling and deforming through the Neogene until today. Five primary input points delivered sediment to the basins along the studied part of the margin. Channels display both axial and transverse orientations, the run‐out lengths of which vary temporally. At various times, relatively coarse‐grained sediment was trapped in the interior basins, occasionally then to be cannibalised during landsliding or erosion of growing structures. At other times, coarse‐grained sediment was bypassed to distal basins or the trench. Multiple sediment input points and occasionally tortuous sediment dispersal corridors result in the evolution of convoluted depositional systems, often with similar styles of sedimentation occurring contemporaneously in proximal and distal basins, contrary to simple models of basin fill. A hierarchy of controls on sediment distribution can be distinguished. At the highest level, sediment distribution is controlled by external factors, for example, glacio‐eustacy and tectonics. At basin scale, the interaction of sedimentary systems with local relief (e.g. evolving seafloor structures and landslides) dictates the location and style of deposition. At the lowest level, autocyclic factors (e.g. flow response to earlier deposits) influence the spatiotemporal variation in erosion and sedimentation. The complex interplay of these factors dictates whether basins were filling, spilling or some combination at any point in time, whilst basins that were filled and spilled may subsequently resume filling due to changes in the bounding conditions. Hence simple use of 'fill and spill' or 'tortuous corridor' models to tectonically active margins is not advised. Furthermore, as sedimentation may influence structure growth, constraining the controls on sediment distribution may improve understanding of the broader evolution of convergent margins and their resource distribution. [ABSTRACT FROM AUTHOR]