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.
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