  We report Keck/ESI and VLT/UVES observations of three super-damped
Lyman-alpha quasar absorbers with H I column densities log N(HI) >= 21.7 at
redshifts z=2-2.5. All three absorbers show similar metallicities (-1.3 to -1.5
dex), and dust depletion of Fe, Ni, and Mn. Two of the absorbers show
supersolar [S/Zn] and [Si/Zn]. We combine our results with those for other DLAs
to examine trends between N(HI), metallicity, dust depletion. A larger fraction
of the super-DLAs lie close to or above the line [X/H]=20.59-log N(HI) in the
metallicity vs. N(HI) plot, compared to the less gas-rich DLAs, suggesting that
super-DLAs are more likely to be rich in molecules. Unfortunately, our data for
Q0230-0334 and Q0743+1421 do not cover H2 absorption lines. For Q1418+0718,
some H2 lines are covered, but not detected. CO is not detected in any of our
absorbers. For DLAs with log N(HI) < 21.7, we confirm strong correlation
between metallicity and Fe depletion, and find a correlation between
metallicity and Si depletion. For super-DLAs, these correlations are weaker or
absent. The absorbers toward Q0230-0334 and Q1418+0718 show potential
detections of weak Ly-alpha emission, implying star formation rates of about
1.6 and 0.7 solar masses per year, respectively (ignoring dust extinction).
Upper limits on the electron densities from C II*/C II or Si II*/Si II are low,
but are higher than the median values in less gas-rich DLAs. Finally, systems
with log N(HI) > 21.7 may have somewhat narrower velocity dispersions delta
v_90 than the less gas-rich DLAs, and may arise in cooler and/or less turbulent
gas.
