The present-day continental slope offshore Brunei Darussalam (NW Borneo) displays several networks of submarine channels possessing planform attributes similar to those observed in better-studied river systems. We use shallow 3D seismic data to study one tributary network in detail. This network is located directly downslope from the shelf-edge Champion Delta and encompasses an area approximately 8 km by 24 km in the strike and dip directions. The channels in this network initiate 1–2 km down dip of the shelf edge and are not directly linked to a terrestrial river system. Mapping of shallow seismic horizons reveals that the tributary channel network is an aggradational feature constructed on top of a relatively smooth slide plane associated with a large mass-failure event. This observation highlights differences between network construction in submarine settings compared to terrestrial settings where tributary networks are net erosional features. The smooth slide plane provides us with the simplest possible initial condition for studying the deposit architecture of an aggradational submarine-channel network. An isopach map between the seafloor and the slide plane is used to unravel sedimentation trends, particularly relative rates of levee and overbank sedimentation as a function of channel relief, lateral distance from the nearest channel centerline, and distance from the shelf edge. We observe an anti-correlation between channel relief and deposit thickness, which suggests that the degree to which currents are confined within channels exerts a first-order control on local deposition rates. We also find that over 80% of the deposit volume associated with the aggradational network is within levees. Observations suggest that this channel network was constructed from turbidity currents that initiated at the shelf edge as sheet flows prior to transitioning down slope into weakly confined flows through the construction of aggradational channels. Thicknesses of channel-forming turbidity currents are estimated using the distance between channel heads and the ratio of channel to overbank deposit thickness. These two methods yield estimates for flow thicknesses that are between 1.1 and 3 times the mean relief of channels in the network.