  CaII 3934,3969 absorbers, which are likely to be a subset of damped Lyman
alpha systems, are the most dusty quasar absorbers known, with an order of
magnitude more extinction in E(B-V) than other absorption systems. There is
also evidence that CaII absorbers trace galaxies with more ongoing
star-formation than the average quasar absorber. Despite this, relatively
little is known in detail about these unusual absorption systems. Here we
present the first high resolution spectroscopic study of 19 CaII quasar
absorbers, in the range 0.6<= z_abs<=1.2, with W3934>=0.2A. Their general
depletion patterns are similar to measurements in the warm halo phase of the
Milky Way and Magellanic Clouds ISM. Dust depletions and alpha-enrichments
profiles of sub-samples of 7 and 3 absorbers, respectively, are measured using
a combination of Voigt profile fitting and apparent optical depth techniques.
Deviations in [Cr/Zn]~0.3+-0.1dex and in [Si/Fe]>~0.8+-0.1dex are detected
across the profile of one absorber, which we attribute to differential dust
depletion. The remaining absorbers have <0.3dex (3sigma limit) variation in
[Cr/Zn], much like the general DLA population, though the dustiest CaII
absorbers remain relatively unprobed in our sample. A limit on electron
densities in CaII absorbers, n_e<0.1cm^-3, is derived using the ratio of
neutral and singly ionised species, assuming a MW-like radiation field. These
electron densities may imply hydrogen densities sufficient for the presence of
molecular hydrogen in the absorbers. The CaII absorber sample comprises a wide
range of velocity widths, v_90=50-470km/s, and velocity structures, thus a
range of physical models for their origin, from simple discs to galactic
outflows and mergers, would be required to explain the observations.
