Three-dimensional bifurcating internal flow is studied for a single mother tube branching into two equal but diverging daughter tubes. The mother tube is straight and of circular cross-section, containing a fully developed incident motion, while the diverging daughters are straight and of semi-circular cross-section. This basic configuration is treated first by direct numerical simulation and secondly by slender-flow modelling, for a variety of Reynolds numbers and angles of divergence. The direct simulations and modelling highlight different forms of three-dimensional separation or flow reversal as well as enhanced upstream and downstream influence and pressure loss induced by the bifurcations especially at increased divergence angles. Comparisons between the results from the simulations and those from the slender-flow modelling show relatively close agreement at medium values of Reynolds number. In particular, as the angle of divergence increases for a given Reynolds number, there is generally first an increase in flow attachment on to the inner divider wall(s) and then, at higher angles, an increasing trend to flow reversal at the corners formed by the junctions of the outer wall with the divider; longitudinal vortex motion is also enhanced then. The agreement persists over a surprisingly wide range of divergence angles.