  We present a detailed study of HI and metals for 110 MgII absorption systems
discovered at 1.98 <= z <= 5.33 in the infrared spectra of high redshift QSOs.
Using new measurements of rest-frame UV lines from optical spectra of the same
targets, we compare the high redshift sample with carefully constructed low
redshift control samples from the literature to study evolutionary trends from
z=0 --> 5.33 (>12 Gyr). We observe a significant strengthening in the
characteristic N(HI) for fixed MgII equivalent width as one moves toward higher
redshift. Indeed at our sample's mean zbar=3.402, all MgII systems are either
damped Ly-alpha absorbers or sub-DLAs, with 40.7% of systems exceeding the DLA
threshold (compared to 16.7% at zbar=0.927). We set lower limits on the
metallicity of the MgII systems where we can measure HI; these results are
consistent with the full DLA population. The classical MgII systems
(W(2796)=0.3-1.0 Ang), which preferentially associate with sub-DLAs, are quite
metal rich at ~0.1 Solar. We applied quantitative classification metrics to our
absorbers to compare with low redshift populations, finding that weak systems
are similar to classic MgII absorbers at low redshift. The strong systems
either have very large MgII and FeII velocity spreads implying non-virialized
dynamics, or are more quiescent DLAs. There is tentative evidence that the
kinetically complex systems evolve in similar fashion to the global star
formation rate. We speculate that if weaker MgII systems represent accreting
gas as suggested by recent studies of galaxy-absorber inclinations, then their
high metal abundance suggests re-accretion of recently ejected material rather
than first-time infall from the metal-poor IGM, even at early times.
