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We present the results of a survey for damped (DLA, log N(H I) > 20.3) andsub-damped Lyman-? systems (19.5 < log N(H I) < 20.3) at z > 2.55 along thelines-of-sight to 77 quasars with emission redshifts in the range 4 < zem <6.3. Intermediate resolution (R ? 4300) spectra have been obtained with theEchellette Spectrograph and Imager (ESI) mounted on the Keck telescope. A totalof 100 systems with log N(H I) > 19.5 are detected of which 40 systems aredamped Lyman-? systems for an absorption length of ?X = 378. About half of thelines of sight of this homogeneous survey have never been investigated forDLAs. We study the evolution with redshift of the cosmological density of theneutral gas and find, consis- tently with previous studies at similarresolution, that ?DLA,H I decreases at z > 3.5. The overall cosmologicalevolution of ?HI shows a peak around this redshift. The H I column densitydistribution for log N(H I) ? 20.3 is ?tted, consistently with previoussurveys, with a single power-law of index ? ? -1.8$\pm$0.25. This power-lawoverpredicts data at the high-end and a second, much steeper, power-law (or agamma function) is needed. There is a flattening of the function at lower H Icolumn densities with an index of ? ? ?1.4 for the column density range log N(HI) = 19.5?21. The fraction of H I mass in sub-DLAs is of the order of 30%. TheH column density distribution does not evolve strongly from z ? 2.5 to z ? 4.5.

Damped and sub-damped Lyman-? absorbers in z > 4 QSOs