Past field investigations suggest that supershear earthquakes occur on simple, smooth fault segments. In contrast, dynamic rupture simulations show how heterogeneity of stress, strength, and fault geometry can trigger supershear transitions, as well as other complex rupture styles. In this work, we analyze an ensemble of thousands of ruptures on randomly generated non-planar fault profiles, published in Fang and Dunham . We aim at documenting the effect of fault roughness and prestress on rupture behavior, emphasizing on supershear transitions. Roughness gives rise to extremely diverse rupture styles, such as rupture arrests and secondary slip pulses that re-rupture previously slipped fault sections. We show that despite a very low prestress, far below the Burridge-Andrews threshold, supershear transitions are also observed. By analyzing the ensemble database in a statistical manner, we demonstrate that supershear transitions are more likely on rougher faults but that sustained supershear propagation tends to occur on smoother fault segments. We also examine specific cases to identify several distinct supershear transition mechanisms and propagation behaviors associated with complex geometry.