  Absorption-selected galaxies offer an effective way to study low-mass
galaxies at high redshift. However, the physical properties of the underlying
galaxy population remains uncertain. In particular, the multiphase
circum-galactic medium is thought to hold key information on gas flows into and
out of galaxies that are vital for galaxy evolution models. Here we present
ALMA observations of CO molecular gas in host galaxies of H_2-bearing
absorbers. In our sample of six absorbers we detect molecular gas-rich galaxies
in five absorber fields although we did not target high-metallicity (>50 per
cent solar) systems for which previous studies reported the highest detection
rate. Surprisingly, we find that the majority of the absorbers are associated
with multiple galaxies rather than single haloes. Together with the large
impact parameters these results suggest that the H_2-bearing gas seen in
absorption is not part of an extended disk, but resides in dense gas pockets in
the circum-galactic and intra-group medium.
