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Absorption-selected galaxies offer an effective way to study low-massgalaxies at high redshift. However, the physical properties of the underlyinggalaxy population remains uncertain. In particular, the multiphasecircum-galactic medium is thought to hold key information on gas flows into andout of galaxies that are vital for galaxy evolution models. Here we presentALMA observations of CO molecular gas in host galaxies of H_2-bearingabsorbers. In our sample of six absorbers we detect molecular gas-rich galaxiesin five absorber fields although we did not target high-metallicity (>50 percent solar) systems for which previous studies reported the highest detectionrate. Surprisingly, we find that the majority of the absorbers are associatedwith multiple galaxies rather than single haloes. Together with the largeimpact parameters these results suggest that the H_2-bearing gas seen inabsorption is not part of an extended disk, but resides in dense gas pockets inthe circum-galactic and intra-group medium.

H_2 molecular gas absorption-selected systems trace CO molecular gas-rich galaxy overdensities