We have investigated the distribution and evolution of ∼3100 intergalactic neutral hydrogen (H i) absorbers with H i column densities log N H i = [12.75, 17.0] at 1.9 < z < 3.2, using 18 high resolution, high signal-to-noise 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 H i column densities of saturated lines, and another using only the Lyα transition. There is no significant difference between the Lyα-only fit and the high-order Lyman fit results. Combining our Lyα-only fit results at 1.7 < z < 3.6 with high-quality 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 H i absorbers at 1.9 < z < 3.2 into two samples, the unenriched forest and the C iv-enriched forest, depending on whether H i lines are associated with C iv at log N C iv ≥ 12.2 within a given velocity range. The entire H i column density distribution function (CDDF) can be described as the combination of these two well-characterised populations which overlap at log N H i ∼ 15. At log N H i ≤ 15, the unenriched forest dominates, showing a similar power-law distribution to the entire forest. The C iv-enriched forest dominates at log N H i ≥ 15, with its distribution function as ∝N ∼−1.45. However, it starts to flatten out at lower N H i , since the enriched forest fraction decreases with decreasing N H i . The deviation from the power law at log N H i = [14, 17] shown in the CDDF for the entire H i sample is a result of combining two different H i populations with a different CDDF shape. The total H i mass density relative to the critical density is Ω H i ∼ 1.6 × 10 −6 h −1 , where the enriched forest accounts for ∼40% of Ω H i .