  Our ability to interpret observations of galaxies and trace their stellar,
gas, and dust content over cosmic time critically relies on our understanding
of how the dust abundance and properties vary with environment. Here, we
compute the dust surface density across cosmic times to put novel constraints
on simulations of the build-up of dust. We provide observational estimates of
the dust surface density consistently measured through depletion methods across
a wide range of environments, going from the Milky Way up to $z=5.5$ galaxies.
These conservative measurements provide complementary estimates to
extinction-based observations. In addition, we introduce the dust surface
density distribution function -- in analogy with the cold gas column density
distribution functions. We fit a power law of the form: $\log f( \Sigma_{\rm
Dust})=-1.92 \times \log \Sigma_{\rm Dust} - 3.65$ which proves slightly
steeper than for neutral gas and metal absorbers. This observed relation, which
can be computed by simulations predicting resolved dust mass functions through
2D projection, provides new constraints on modern dust models.
