  Among the key parameters defining the ISM of galaxies is the fraction of the
metals that are locked up in dust: the metals-to-dust ratio. This ratio bears
not only on the ISM and its evolution, but particularly on the origin of cosmic
dust. We combine extinction and abundance data from GRB afterglows, from QSO
absorbers, as well as from galaxy-lensed QSOs, to determine the metals-to-dust
ratios for lines-of-sight through a wide diversity of galaxies from blue, dwarf
starbursts to massive ellipticals, across a vast range in redshift z=0.1-6.3,
and nearly three orders of magnitude in column density and metal abundance. We
thus determine the metals-to-dust ratio in a unique way, providing direct
determinations of in situ gas and dust columns without recourse to assumptions
with large uncertainties. We find that the metals-to-dust ratios in these
systems are surprisingly close to the value for the local group (10^{21.3} cm-2
A_V mag-1), with a mean value of 10^{21.2} cm-2 A_V mag-1 and a standard
deviation of 0.3 dex. There is no evidence of deviation from this mean ratio as
a function of metallicity, even down to our lowest metallicity of 0.01 Z/Z_sun.
The lack of any obvious dependence of the metals-to-dust ratio on either column
density, galaxy type or age, redshift, or metallicity indicates a close
correspondence between the formation of the metals and the formation of dust.
Any delay between the formation of metals and dust must be shorter than the
typical metal-enrichment times of these galaxies. Formation of the bulk of the
dust in low mass stars is therefore ruled out by these data at any cosmic
epoch. Furthermore, dust destruction must not dominate over formation/growth in
virtually any galaxy environment. The correlation between metals and dust is a
natural consequence of the formation of the bulk of dust in SNe [Abridged].
