  The "torus" obscurer of Active Galactic Nuclei (AGN) is poorly understood in
terms of its density, substructure and physical mechanisms. Large X-ray surveys
provide model boundary constraints, for both Compton-thin and Compton-thick
levels of obscuration, as obscured fractions are mean covering factors
$f_{\text{cov}}$. However, a major remaining uncertainty is host galaxy
obscuration. In Paper I we discovered a relation of $N_H \propto
M_{\star}^{1/3}$ for the obscuration of galaxy-scale gas. Here we apply this
observational relation to the AGN population, and find that galaxy-scale gas is
responsible for a luminosity-independent fraction of Compton-thin AGN, but does
not produce Compton-thick columns. With the host galaxy obscuration understood,
we present a model of the remaining, nuclear obscurer which is consistent with
a range of observations. Our radiation-lifted torus model consists of a
Compton-thick component ($f_{\text{cov}}\sim35\%$) and a Compton-thin component
($f_{\text{cov}}\sim40\%$), which depends on both black hole mass and
luminosity. This provides a useful summary of observational constraints for
torus modellers who attempt to reproduce this behaviour. It can also be
employed as a sub-grid recipe in cosmological simulations which do not resolve
the torus. We also investigate host-galaxy X-ray obscuration inside
cosmological, hydro-dynamic simulations (EAGLE, Illustris). The obscuration
from ray-traced galaxy gas can agree with observations, but is highly sensitive
to the chosen feedback assumptions.
