We use spectral stacking to measure the contribution of galaxies of different masses and in different hierarchies to the cosmic atomic hydrogen ( HI ) mass density in the local Universe . Our sample includes 1793 galaxies at z < 0.11 observed with the Westerbork Synthesis Radio Telescope , for which Sloan Digital Sky Survey spectroscopy and hierarchy information are also available . We find a cosmic HI mass density of \Omega _ { HI } = ( 3.99 \pm 0.54 ) \times 10 ^ { -4 } h _ { 70 } ^ { -1 } at \langle z \rangle = 0.065 . For the central and satellite galaxies , we obtain \Omega _ { HI } of ( 3.51 \pm 0.49 ) \times 10 ^ { -4 } h _ { 70 } ^ { -1 } and ( 0.90 \pm 0.16 ) \times 10 ^ { -4 } h _ { 70 } ^ { -1 } , respectively . We show that galaxies above and below stellar masses of \sim 10 ^ { 9.3 } M _ { \odot } contribute in roughly equal measure to the global value of \Omega _ { HI } . While consistent with estimates based on targeted HI surveys , our results are in tension with previous theoretical work . We show that these differences are , at least partly , due to the empirical recipe used to set the partition between atomic and molecular hydrogen in semi-analytical models . Moreover , comparing our measurements with the cosmological semi-analytic models of galaxy formation Shark and GALFORM reveals gradual stripping of gas via ram pressure works better to fully reproduce the properties of satellite galaxies in our sample , than strangulation . Our findings highlight the power of this approach in constraining theoretical models , and confirm the non-negligible contribution of massive galaxies to the HI mass budget of the local Universe .