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We report the bivariate HI- and H$_2$-stellar mass distributions of localgalaxies in addition of an inventory of galaxy mass functions, MFs, for HI,H$_2$, cold gas, and baryonic mass, separately into early- and late-typegalaxies. The MFs are determined using the HI and H$_2$ conditionaldistributions and the galaxy stellar mass function, GSMF. For the conditionaldistributions we use the compilation presented in Calette et al. 2018. Fordetermining the GSMF from $M_{\ast}\sim3\times10^{7}$ to $3\times10^{12}$$M_{\odot}$, we combine two spectroscopic samples from the SDSS at the redshiftrange $0.0033<z<0.2$. We find that the low-mass end slope of the GSMF, aftercorrecting from surface brightness incompleteness, is $\alpha\approx-1.4$,consistent with previous determinations. The obtained HI MFs agree with radioblind surveys. Similarly, the H$_2$ MFs are consistent with CO follow-upoptically-selected samples. We estimate the impact of systematics due tomass-to-light ratios and find that our MFs are robust against systematicerrors. We deconvolve our MFs from random errors to obtain the intrinsic MFs.Using the MFs, we calculate cosmic density parameters of all the baryoniccomponents. Baryons locked inside galaxies represent 5.4% of the universalbaryon content, while $\sim96$% of the HI and H$_2$ mass inside galaxies residein late-type morphologies. Our results imply cosmic depletion times of H$_2$and total neutral H in late-type galaxies of $\sim 1.3$ and 7.2 Gyr,respectively, which shows that late type galaxies are on average inefficient inconverting H$_2$ into stars and in transforming HI gas into H$_2$. Our resultsprovide a fully self-consistent empirical description of galaxy demographics interms of the bivariate gas--stellar mass distribution and their projections,the MFs. This description is ideal to compare and/or to constrain galaxyformation models.

The bivariate gas-stellar mass distributions and the mass functions of early- and late-type galaxies at $z\sim0$