ABSTRACTWe extend our previous work focused at z ∼ 0, studying the redshift evolution of galaxy dynamical properties using the state-of-the-art semi-analytic model GAEA (GAlaxy Evolution and Assembly): we show that the predicted size–mass relation for discy/star-forming and quiescent galaxies is in good agreement with observational estimates, up to z ∼ 2. Bulge-dominated galaxies have sizes that are offset low with respect to observational estimates, mainly due to our implementation of disc instability at high redshift. At large masses, both quiescent and bulge-dominated galaxies have sizes smaller than observed. We interpret this as a consequence of our most massive galaxies having larger gas masses than observed, and therefore being more affected by dissipation. We argue that a proper treatment of quasar-driven winds is needed to alleviate this problem. Our model compact galaxies have number densities in agreement with observational estimates and they form most of their stars in small and low angular momentum high-z haloes. GAEA predicts that a significant fraction of compact galaxies forming at high-z is bound to merge with larger structures at lower redshifts: therefore they are not the progenitors of normal-size passive galaxies at z = 0. Our model also predicts a stellar–halo size relation that is in good agreement with observational estimates. The ratio between stellar size and halo size is proportional to the halo spin and does not depend on stellar mass but for the most massive galaxies, where active galactic nucleus feedback leads to a significant decrease of the retention factor (from about 80 per cent to 20 per cent).