  We have investigated the distribution and evolution of ~3100 intergalactic HI
absorbers with HI column densities log N(HI) = [12.75, 17.0] at 1.9 < z < 3.2,
using 18 high resolution, high S/N quasar spectra obtained from the ESO
VLT/UVES archive. We used two sets of Voigt profile fitting analysis, one
including all the available high-order Lyman lines to obtain reliable HI column
densities of saturated lines, and another using only the Ly-alpha lines. There
is no significant difference between the results from the two fits. Combining
our results with literature data, the mean number density at 0 < z < 4 is not
well described by a single power law and strongly suggests that its evolution
slows down at z < 1.5 at the high and low column density ranges. We also
divided our entire HI absorbers at 1.9 < z < 3.2 into two samples, the
unenriched forest and the CIV-enriched forest, depending on whether HI lines
are associated with CIV at log N(CIV) > 12.2 within a given velocity range. The
entire HI column density distribution function (CDDF) can be described as the
combination of these two well-characterised populations which overlap at log
N(HI) ~ 15. At log N(HI) < 15, the unenriched forest dominates, showing a
similar power-law distribution to the entire forest. The CIV-enriched forest
dominates at log N(HI) > 15, with its distribution function proportional to
N(HI)^(-1.45). However, it starts to flatten out at lower N(HI), since the
enriched forest fraction decreases with decreasing N(HI). The deviation from
the power law at log N(HI) = [14, 17] shown in the CDDF for the entire HI
sample is a result of combining two different HI populations with a different
CDDF shape. The total HI mass density relative to the critical density is
Omega(HI) ~ 1.6 x 10^(-6) h^(-1), where the enriched forest accounts for ~40%
of Omega(HI).
