  Quasar absorbers provide a powerful observational tool with which to probe
both galaxies and the intergalactic medium up to high redshift. We present a
study of the evolution of the column density distribution, f(N,z), and total
neutral hydrogen mass in high-column density quasar absorbers using data from a
recent high-redshift survey for damped Lyman-alpha (DLA) and Lyman limit system
(LLS) absorbers. Whilst in the redshift range 2 to 3.5, ~90% of the neutral HI
mass is in DLAs, we find that at z>3.5 this fraction drops to only 55% and that
the remaining 'missing' mass fraction of the neutral gas lies in sub-DLAs with
N(HI) 10^{19} - 2 * 10^{20} cm^{-2}.
