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The recently discovered population of ultra‐faint extended line emitters, with fluxes of a few times  10 −18  erg s −1  cm −2   at   z ∼ 3 , can account for the majority of the incidence rate of damped Lyα systems (DLAs) at this redshift if the line emission is interpreted as Lyα. We show here that a model similar to that proposed by Haehnelt, Steinmetz &amp; Rauch (2000), which reproduces the incidence rate and kinematics of DLAs in the context of Λ cold dark matter models for structure formation, also reproduces the size distribution of the new population of faint Lyα emitters for plausible parameters. This lends further support to the interpretation of the emission as Lyα, as well as the identification of the emitters with the hitherto elusive population of DLA host galaxies. The observed incidence rate of DLAs together with the observed space density and size distribution of the emitters suggest a duty cycle of  ∼0.2–0.4  for the Lyα emission from DLA host galaxies. We further show that Lyα cooling is expected to contribute little to the Lyα emission for the majority of emitters. This leaves centrally concentrated star formation at a rate of a few tenths  M ⊙  yr −1  , surrounded by extended Lyα haloes with radii up to 30–50 kpc, as the most plausible explanation for the origin of the emission. Both the luminosity function of Lyα emission and the velocity width distribution of low ionization absorption require that galaxies inside dark matter (DM) haloes with virial velocities  ≲50–70 km s −1   contribute little to the incidence rate of DLAs at   z ∼ 3 , suggesting that energy and momentum input due to star formation efficiently removes gas from these haloes. Galaxies with DM haloes with virial velocities of  100–150 km s −1   appear to account for the majority of DLA host galaxies. DLA host galaxies at   z ∼ 3  should thus become the building blocks of typical present‐day galaxies like our Milky Way.

A joint model for the emission and absorption properties of damped Lyα absorption systems