Ca ii \lambda \lambda 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 Ca ii 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 Ca ii quasar absorbers , in the range 0.6 \leq z _ { abs } \leq 1.2 , with Ca ii \lambda 3934 equivalent widths , W _ { 0 } ^ { 3934 } \geq 0.2 \AA . Their general elemental depletion patterns are found to be similar to measurements in the warm halo phase of the Milky Way ( MW ) and Magellanic Clouds interstellar medium . 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 ] } \sim 0.3 \pm 0.1 dex and in { [ Si / Fe ] } \gtrsim 0.8 \pm 0.1 dex are detected across the profile of one absorber , which we attribute to differential dust depletion . The remaining absorbers have < 0.3 dex ( 3 \sigma limit ) variation in [ Cr/Zn ] , much like the general DLA population , though the dustiest Ca ii absorbers , those with W _ { 0 } ^ { 3934 } > 0.7 \AA , remain relatively unprobed in our sample . A limit on electron densities in Ca ii absorbers , n _ { e } < 0.1 cm ^ { -3 } , is derived using the ratio of neutral and singly ionised species and assuming a MW-like radiation field . These electron densities may imply hydrogen densities sufficient for the presence of molecular hydrogen in the absorbers . The Ca ii absorber sample comprises a wide range of velocity widths , \Delta v _ { 90 } = 50 - 470 km s ^ { -1 } , 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 .