We study metal depletion due to dust in the interstellar medium ( ISM ) to infer the properties of dust grains and characterize the metal and dust content of galaxies down to low metallicity and intermediate redshift z . We provide metal column densities and abundances of a sample of 70 damped Lyman- \alpha absorbers ( DLAs ) towards quasars , observed at high spectral resolution with the Very Large Telescope ( VLT ) Ultraviolet and Visual Echelle Spectrograph ( UVES ) . This is the largest sample of phosphorus abundances measured in DLAs so far . We use literature measurements for Galactic clouds to cover the high-metallicity end . We discover tight ( scatter \lesssim 0.2 dex ) correlations between [ Zn/Fe ] and the observed relative abundances from dust depletion . This implies that grain growth in the ISM is an important process of dust production . These sequences are continuous in [ Zn/Fe ] from dust-free to dusty DLAs , and to Galactic clouds , suggesting that the availability of refractory metals in the ISM is crucial for dust production , regardless of the star formation history . We observe [ S/Zn ] up to \sim 0.25 dex in DLAs , which is broadly consistent with Galactic stellar abundances . Furthermore , we find a good agreement between the nucleosynthetic pattern of Galactic halo stars and our observations of the least dusty DLAs . This supports recent star formation in low-metallicity DLAs . The derived depletions of Zn , O , P , S , Si , Mg , Mn , Cr , and Fe correlate with [ Zn/Fe ] , with steeper slopes for more refractory elements . P is mostly not affected by dust depletion . We present canonical depletion patterns to be used as reference in future studies of relative abundances and depletion . We derive the total ( dust-corrected ) metallicity , typically -2 \lesssim [ M /H ] _ { tot } \lesssim 0 for DLAs , and scattered around solar metallicity for the Galactic ISM . The dust-to-metal ratio ( \mathcal { { DT M } } ) increases with metallicity , again supporting the importance of grain growth for dust production . The dust extinction A _ { V } derived from the depletion is typically < 0.2 mag in DLAs . Finally , we derive elemental abundances in dust , which is key to understanding the dust composition and its evolution . We observe similar abundances of Mg , Si , and Fe in dust ; this suggests that grain species such as pyroxenes and iron oxides are more important than olivine , but this needs to be confirmed by more detailed analysis . Overall , we characterize dust depletion , nucleosynthesis , and dust-corrected metallicity in DLAs , providing a unified picture from low-metallicity systems to the Galactic ISM .