ABSTRACT We have updated the Munich galaxy formation model, L-galaxies, to follow the radial distributions of stars and atomic and molecular gas in galaxy discs. We include an H2-based star-formation law, as well as a detailed chemical-enrichment model with explicit mass-dependent delay times for SN-II, SN-Ia, and AGB stars. Information about the star formation, feedback, and chemical-enrichment histories of discs is stored in 12 concentric rings. The new model retains the success of its predecessor in reproducing the observed evolution of the galaxy population, in particular, stellar mass functions and passive fractions over the redshift range 0 ≤ z ≤ 3 and mass range $8\le \log (M_*/\hbox{$\rm \, M_{\odot }$})\le 12$, the black hole-bulge mass relation at z = 0, galaxy morphology as a function of stellar mass and the mass–metallicity relations of both stellar and gas components. In addition, its detailed modelling of the radial structure of discs allows qualitatively new comparisons with observation, most notably with the relative sizes and masses of the stellar, atomic, and molecular components in discs. Good agreement is found with recent data. Comparison of results obtained for simulations differing in mass resolution by more than two orders of magnitude shows that all important distributions are numerically well converged even for this more detailed model. An examination of metallicity and surface-density gradients in the stars and gas indicates that our new model, with star formation, chemical enrichment, and feedback calculated self-consistently on local disc scales, reproduces some but not all of the trends seen in recent many-galaxy IFU surveys.