The onset condition of flow separation in diverging tee junctions was investigated numerically. Flow separation and recirculation at the proximal region of a bypass graft can contribute to early phase graft failure in aortocoronary bypass (ACB) surgery. Rounding the inlet edge of the branch reduces the likelihood of flow separation and recirculation. The recirculating zone at the upstream end of the branch is fully eliminated when a threshold value of mass flow rate ratio is reached. The corresponding flow characteristics obtained from diverging tees with a diameter ratio <= 0.2 and a radius of curvature <= 0.25 for a Reynolds number <= 1817 indicate that an increasing flow rate ratio induces an exponential decrease in the recirculation length. An increase in the diameter ratio and Reynolds number increases both the onset condition of the flow separation and the recirculation length at the upstream end of the branch. However, a decrease in the diameter ratio reduces the onset condition of separation more effectively than a decrease in the radius of curvature at the junction.