We have obtained high signal:to:noise optical spectroscopy at 5AA resolution of 27 quasars from the APM z$>$4 quasar survey. The spectra have been analyzed to create new samples of high redshift Lyman-limit and damped Lyman-$alpha$ absorbers. These data have been combined with published data sets in a study of the redshift evolution and the column density distribution function for absorbers with $log$N(HI)$ge17.5$, over the redshift range 0.01 $<$ z $<$ 5. The main results are: begin{itemize} item Lyman limit systems: The data are well fit by a power law $N(z) = N_0(1 + z)^{gamma}$ for the number density per unit redshift. For the first time intrinsic evolution is detected in the product of the absorption cross-section and comoving spatial number density for an $Omega = 1$ Universe. We find $gamma = 1.55$ ($gamma = 0.5$ for no evolution) and $N_0 = 0.27$ with $>$99.7% confidence limits for $gamma$ of 0.82 & 2.37. item Damped lya systems: The APM QSOs provide a substantial increase in the redshift path available for damped surveys for $z>3$. Eleven candidate and three confirmed damped Ly$alpha$ absorption systems, have been identified in the APM QSO spectra covering the redshift range $2.8le z le 4.4$ (11 with $z>3.5$). Combining the APM survey confirmed and candidate damped lya absorbers with previous surveys, we find evidence for a turnover at z$sim$3 or a flattening at z$sim$2 in the cosmological mass density of neutral gas, $Omega_g$. end{itemize} The Lyman limit survey results are published in Storrie-Lombardi, et~al., 1994, ApJ, 427, L13. Here we describe the results for the DLA population of absorbers.
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