Abstract Transform and passive margins developed during the continental rifting and opening of oceanic basins are fundamental elements of plate tectonics. It has been suggested that inherited structures, plate divergence velocities and surface processes exert a first-order control on the topographic and bathymetric evolution and thermal history of these margins and related sedimentary basins. Their complex spatial-temporal dynamics have remained controversial. Here, we conducted 3D magmatic-thermo-mechanical numerical experiments coupled with surface processes modelling to simulate the dynamics of continental rifting, continental transform fault zone formation as well as persistent oceanic transform faulting and zero-offset oceanic fracture zones development. Numerical modelling results allow to explain the first-order observations from passive and transform margins, such as diachronous rifting, heat flow rise and cooling in individual depocentres as well as contrasting basin tectonics of extensional and transtensional origin. In addition, the models reproduce the rise of both marginal ridges and transform marginal plateaus, and their interaction with erosion and sedimentation. Comparison of model results with observations from natural examples yields new insights into the tectono-sedimentary and thermal evolution of several key passive and transform continental margins worldwide.