  A growing body of evidence suggests that part of, if not all, scattering
regions of active galactic nuclei (AGNs) are clumpy. Hence. in this paper, we
run radiative transfer models in the optical/UV for a variety of AGN
reprocessing regions with different distributions of clumpy scattering media.
We use the latest version of the Monte Carlo code STOKES presented in the first
two papers of this series to model AGN reprocessing regions of increasing
morphological complexity. We replace previously uniform-density media with up
to thousands of constant-density clumps. We couple a continuum source to
fragmented equatorial scattering regions, polar outflows, and toroidal,
obscuring dust regions and investigate a wide range of geometries. We also
consider different levels of fragmentation in each scattering region to
evaluate importance of fragmentation for the net polarization of the AGN. We
find that, in comparison with uniform-density models, equatorial distributions
of gas and dust clouds result in grayer spectra, and show a decrease of the net
polarization percentage at all lines of sight. The resulting polarization
position angle depends on the morphology of the clumpy structure, with extended
tori favoring parallel polarization while compact tori produce orthogonal
polarization position angles. In the case of polar scattering regions,
fragmentation increases the net polarization unless the cloud filling factor is
small. A complete set of AGN models constructed from the individual, fragmented
regions is investigated. Our modeling shows that the introduction of fragmented
dusty tori significantly alters the resulting net polarization of an AGN.
Comparison of our models to polarization observations of large AGN samples
greatly favors geometrically compact clumpy tori over extended ones.
