Unsteady flow through diverging tees is of interest in many industrial systems and physiological applications. In this study, the characteristics of the transient flow behaviors at the junctions of diverging tees with sharp- and round-edge junctions were investigated numerically based on physiological boundary conditions. The flow conditions were characterized based on a Newtonian fluid analogous to blood with a Womersley number of 23.13 and a mean inlet Reynolds number of 652. The results from this study demonstrate the onset conditions of flow separation at the upstream end of both branches and the relationship between the axial and secondary flow fields. For both junctions, the onset condition of separation and the strength of recirculation correspond closely to the momentum of the secondary boundary layer adjacent to the inner-wall of the branch. The nature of the boundary layer is strongly dependent on the structures of the vortical cells. The round-edge junction attenuates the strength of recirculation by triggering flow separation at a much lower flow rate ratio. The strength of the recirculation was found to be inversely proportional to the strength of the secondary flow. The reduction of the strength of recirculation leads to an increase in wall shear stress level and a decrease in oscillation effects.