  Context. From stars to active galactic nuclei, many astrophysical systems are
surrounded by an equatorial distribution of dusty material that are, in a
number of cases, spatially unresolved even with cutting edge facilities. Aims.
In this paper, we investigate if and how one can determine the unresolved and
heterogeneous morphology of dust distribution around a central bright source
using time-resolved polarimetric observations. Methods. We use polarized
radiative transfer simulations to study a sample of circumnuclear dusty
morphologies. We explore a grid of uniform, fragmented, density-stratified,
geometrically-variable models in the near-infrared, optical and ultraviolet
bands, and present their distinctive time-dependent polarimetric signatures.
Results. As expected, varying the structure of the obscuring equatorial disk
has a deep impact on the inclination-dependent flux, polarization degree and
angle, and time-lags we observe. We find that stratified media are
distinguishable by time-resolved polarimetric observations, and that the
expected polarization is much higher in the infrared band than in the
ultraviolet. However, due to the physical scales imposed by dust sublimation,
the average time-lags between the total and polarized fluxes are important
(months to years), lengthening the observational campaigns necessary to break
more sophisticated (and therefore also more degenerated) models. In the
ultraviolet band, time-lags are slightly shorter than in the infrared or
optical bands, and, coupled to lower diluting starlight fluxes, time-resolved
polarimetry in the UV appears more promising for future campaigns.
