Absorption-selected galaxies trace the low-mass, late-type, star-forming population at $z \sim 2-3$

We report on the stellar content, half-light radii and star formation rates of seven new and three known high redshift (z>2) galaxies detected as strong neutral hydrogen (HI) absorbers (Damped Ly-alpha Absorbers (DLAs) and sub-DLAs) toward background quasars. We study the their galactic environments, and perform the first systematic morphological characterisation of such absorption-emission pairs at high redshifts. Leveraging the spatial resolution of the Hubble Space Telescope (HST) Wide Field Camera 3, and careful Point Spread Function subtraction we image the counterparts of the absorbers in the F606W, F105W, and F160W filters. Our analysis reveals complex, irregular hosts with multiple star-forming clumps. At a drizzled spatial resolution of 0.067 arcsec/pxl, 40% of our absorption-selected sample requires multiple Sersic components for an accurate modelling of the observed galaxy light distributions. We measure half-light radii in the range r_1/2 ~ 0.4 - 2.6 kpc based on the reddest band (F160W) to trace the oldest stellar populations, and stellar masses in the range log M*[Msun] ~ 8 - 10 derived from spectral energy distribution (SED) fits to the broadband HST photometry. Spectroscopic- and SED-based star formation rates are largely consistent, and lie in the range log SFR [Msun/yr] = -0.06 - 1.7. Placed on the mass-size relation and on the main sequence of star forming galaxies, we find that an absorption-selection at high redshift extends known relations determined from deep luminosity-selected surveys to an order of magnitude less massive galaxies, primarily composed of star forming late-types.