Abstract Finite-element models of neotectonics require transform faults to rupture seismically even where preseismic shear stresses are low, presumably by dynamic-weakening mechanisms. A long-standing objection is that, if a rupture initiated at an asperity with high static friction stresses, which then transitioned to low dynamic-weakening stresses, local stress drop would be near total and on the order of 80 MPa, which is 4×–40× greater than observed. But the 5 Mw ≥ 7.8 transform earthquakes since 2000 initially ruptured on the branch faults of small net slip (Stein and Bird, 2024). If the slip initiates on a branch fault with different slip physics and no dynamic weakening, this solves the stress-drop problem. We propose that most large shallow earthquakes are hybrid ruptures, which begin on branch faults of small slip with high shear stresses, and then continue propagating on a connected dynamically weakened fault of large slip, even where shear stresses are low. One prediction of this model is that most large shallow ruptures should be unilateral. We test this prediction against the 100 largest (m ≥ 6.49) shallow continental strike-slip earthquakes 1977–2022, using information from the Global Centroid Moment Tensor and International Seismological Centre catalogs. The differences in time and location between the epicenter and the epicentroid define a horizontal “migration” velocity vector for the evolving centroid of each rupture. Early aftershock locations are summarized by a five-parameter elliptical model. Using the geometric relations between these (and mapped traces of active faults) and guided by a symmetrical decision table, we classified 55 ruptures as apparently unilateral, 30 as bilateral, and 15 as ambiguous. Our finding that a majority (55%–70%) of these ruptures are unilateral permits the interpretation that a majority of ruptures are hybrids, both in terms of geometry (branch fault to transform) and in terms of the physics of their fault slip.