The stellar and neutral hydrogen (HI) mass functions at z~0 are fundamental benchmarks for current models of galaxy evolution. A natural extension of these benchmarks is the two-dimensional distribution of galaxies in the plane spanned by stellar and HI mass, which provides a more stringent test of simulations, as it requires the HI to be located in galaxies of the correct stellar mass. Combining HI data from the ALFALFA survey, with optical data from SDSS, we find a distinct envelope in the HI-to-stellar mass distribution, corresponding to an upper limit in the HI fraction that varies monotonically over five orders of magnitude in stellar mass. This upper envelope in HI fraction does not favour the existence of a significant population of dark galaxies with large amounts of gas but no corresponding stellar population. The envelope shows a break at a stellar mass of ~10^9 Msun, which is not reproduced by modern models of galaxy populations tracing both stellar and gas masses. The discrepancy between observations and models suggests a mass dependence in gas storage and consumption missing in current galaxy evolution prescriptions. The break coincides with the transition from galaxies with predominantly irregular morphology at low masses to regular disks at high masses, as well as the transition from cold to hot accretion of gas in simulations.
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