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We study the evolution of the scaling relations between the maximum circular velocity, stellar mass and optical half‐light radius of star‐forming disc‐dominated galaxies in the context of  Λ  cold dark matter‐based galaxy formation models. Using data from the literature combined with new data from the Deep Extragalactic Evolutionary Probe 2 (DEEP2) and All‐wavelength Extended Groth Strip International Survey (AEGIS) surveys, we show that there is a consistent picture for the evolution of these scaling relations from   z ∼ 2  to   z = 0 , both observationally and theoretically. The evolution of the observed stellar scaling relations is weaker than that of the virial scaling relations of dark matter haloes, which can be reproduced, both qualitatively and quantitatively, with a simple, cosmologically motivated model for disc evolution inside growing Navarro–Frenk–White dark matter haloes. In this model optical half‐light radii are smaller, both at fixed stellar mass and at maximum circular velocity, at higher redshifts. This model also predicts that the scaling relations between baryonic quantities (baryonic mass, baryonic half‐mass radii and maximum circular velocity) evolve even more weakly than the corresponding stellar relations. We emphasize, though, that this weak evolution does not imply that individual galaxies evolve weakly. On the contrary, individual galaxies grow strongly in mass, size and velocity but in such a way that they move largely along the scaling relations. Finally, recent observations have claimed surprisingly large sizes for a number of star‐forming disc galaxies at   z ≃ 2 , which has caused some authors to suggest that high‐redshift disc galaxies have abnormally high spin parameters. However, we argue that the disc scalelengths in question have been systematically overestimated by a factor of  ∼2  and that there is an offset of a factor of  ∼1.4  between H α  sizes and optical sizes. Taking these effects into account, there is no indication that star‐forming galaxies at high redshifts (  z ≃ 2 ) have abnormally high spin parameters.

On the evolution of the velocity–mass–size relations of disc‐dominated galaxies over the past 10 billion years