  Context. Several issues regarding the nature of dust at high redshift remain
unresolved: its composition, its production and growth mechanisms, and its
effect on background sources. Aims. We provide a more accurate relation between
dust depletion levels and dust-to-metals ratio (DTM), and to use the DTM to
investigate the origin and evolution of dust in the high-redshift Universe via
Gamma-ray burst damped Lyman-alpha absorbers (GRB-DLAs). Methods. We use
absorption-line measured metal column densities for a total of 19 GRB-DLAs,
including five new GRB afterglow spectra from VLT/X-shooter. We use the latest
linear models to calculate the dust depletion strength factor in each DLA.
Using these values we calculate total dust and metal column densities to
determine a DTM. We explore the evolution of DTM with metallicity, and compare
it to previous trends in DTM measured with different methods. Results. We find
significant dust depletion in 16 of our 19 GRB-DLAs, yet 18 of the 19 have a
DTM significantly lower than the Milky Way. We find that DTM is positively
correlated with metallicity, which supports a dominant ISM grain-growth mode of
dust formation. We find a substantial discrepancy between the dust content
measured from depletion and that derived from the total V-band extinction,
$A_V$ , measured by fitting the afterglow SED. We advise against using a
measurement from one method to estimate that from the other until the
discrepancy can be resolved.
