Recent multiscale simulations have made it possible to follow gas inflows responsible for high-Eddington ratio accretion on to massive black holes (BHs) from galactic scales to the BH accretion disc. When sufficient gas is driven towards a BH, gravitational instabilities generically form lopsided, eccentric discs that propagate inwards from larger radii. The lopsided stellar disc exerts a strong torque on the gas, driving inflows that fuel the growth of the BH. Here, we investigate the possibility that the same disc, in its gas-rich phase, is the putative ‘torus’ invoked to explain obscured active galactic nuclei (AGN) and the cosmic X-ray background. The disc is generically thick and has characteristic ∼1–10 pc sizes and masses resembling those required of the torus. Interestingly, the scale heights and obscured fractions of the predicted torii are substantial even in the absence of strong stellar feedback providing the vertical support. Rather, they can be maintained by strong bending modes and warps/twists excited by the inflow-generating instabilities. A number of other observed properties commonly attributed to ‘feedback’ processes may in fact be explained entirely by dynamical, gravitational effects: the lack of alignment between torus and host galaxy, correlations between local star formation rate (SFR) and turbulent gas velocities and the dependence of obscured fractions on AGN luminosity or SFR. We compare the predicted torus properties with observations of gas surface density profiles, kinematics, scale heights and SFR densities in AGN, and find that they are consistent in all cases. We argue that it is not possible to reproduce these observations and the observed column density distribution without a clumpy gas distribution, but allowing for simple clumping on small scales the predicted column density distribution is in good agreement with observations from NH∼ 1020–1027 cm−2. We examine how the NH distribution scales with galaxy and AGN properties. The dependence is generally simple, but AGN feedback may be necessary to explain certain trends in obscured fraction with luminosity and/or redshift. In our paradigm, the torus is not merely a bystander or passive fuel source for accretion, but is itself the mechanism driving accretion. Its generic properties are not coincidence, but requirements for efficient accretion.