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The division of sediment at river bifurcations is crucial for the morphodynamics of anastamosing rivers and distributary delta channel networks. Many river bifurcations are strongly asymmetric and have a planform were a small channel branches off to the side. Such a configuration is also typical for man‐made diversions of water and sediment into canals. At asymmetric bifurcations, the division of sediment is influenced by the secondary current, which is caused by the turning of the flow towards the side. The secondary currents cause especially water from the lower parts of the water column to be diverted into the side branch. As the sediment concentration close to the bottom is high, side branches can receive a disproportionately large fraction of the incoming sediment load, relative to the water discharge. Lateral diversions have been extensively studied with physical and numerical experiments, with the goal to either mitigate or exploit this effect. However, a systematic mathematical analysis of the parameter space has not yet appeared in the literature. Here, we present a comprehensive analysis by way of an idealized model, revealing how the division of sediment is influenced by the width and depth of the branches. We show that the excess of sediment that is diverted into the side branch is lower when the inlet to the side branch is wider and shallower. This may have larger implications for the stability of delta channel networks, as inlets to side branches tend to be locally wider, which likely contributes to their morphological stability.