We compare the semi-analytic models of galaxy formation of Fu et al. which track the evolution of the radial profiles of atomic and molecular gas in galaxies, with gas fraction scaling relations derived from a stellar mass-limited sample of 299 galaxies from the CO Legacy Database for GASS. These galaxies have measurements of the CO(1–0) line from the IRAM 30-m telescope and the H i line from Arecibo, as well as measurements of star formation rates, stellar masses, galaxy sizes and concentration parameters from GALEX+SDSS photometry. The models provide a good description of how condensed baryons in star-forming galaxies are partitioned into atomic and molecular gas and stars as a function of galaxy stellar mass and stellar surface density. The models do not reproduce the observed tight relation between stellar surface mass density and bulge-to-disc ratio in these galaxies. The current implementation of ‘radio-mode feedback’ in the models produces trends that disagree strongly with the data. In the models, gas cooling shuts down in nearly all galaxies in dark matter haloes above a mass of ∼1012 M⊙. As a result, stellar mass is the observable that best predicts whether a galaxy has little or no neutral gas, that is, whether a galaxy has been quenched. In contrast, our data show that quenching is largely independent of stellar mass. Instead, there are clear thresholds in bulge-to-disc ratio and in stellar surface density that demarcate the location of quenched galaxies in our chosen parameter space. We speculate that the disagreement between the models and the observations may be resolved if radial transport of gas from the outer disc is included as an additional bulge formation mechanism in the models. In addition, we propose that processes associated with bulge formation play a key role in depleting the neutral gas in galaxies and that gas accretion is suppressed in a significant fraction of galaxies following the formation of the bulge, even in dark matter haloes of low mass.