  Using 3D AMR simulations, linking the 50 kpc to the sub-pc scales over the
course of 40 Myr, we systematically relax the classic Bondi assumptions in a
typical galaxy hosting a SMBH. In the realistic scenario, where the hot gas is
cooling, while heated and stirred on large scales, the accretion rate is
boosted up to two orders of magnitude compared with the Bondi prediction. The
cause is the nonlinear growth of thermal instabilities, leading to the
condensation of cold clouds and filaments when t_cool/t_ff < 10. Subsonic
turbulence of just over 100 km/s (M > 0.2) induces the formation of thermal
instabilities, even in the absence of heating, while in the transonic regime
turbulent dissipation inhibits their growth (t_turb/t_cool < 1). When heating
restores global thermodynamic balance, the formation of the multiphase medium
is violent, and the mode of accretion is fully cold and chaotic. The recurrent
collisions and tidal forces between clouds, filaments and the central clumpy
torus promote angular momentum cancellation, hence boosting accretion. On
sub-pc scales the clouds are channelled to the very centre via a funnel. A good
approximation to the accretion rate is the cooling rate, which can be used as
subgrid model, physically reproducing the boost factor of 100 required by
cosmological simulations, while accounting for fluctuations. Chaotic cold
accretion may be common in many systems, such as hot galactic halos, groups,
and clusters, generating high-velocity clouds and strong variations of the AGN
luminosity and jet orientation. In this mode, the black hole can quickly react
to the state of the entire host galaxy, leading to efficient self-regulated AGN
feedback and the symbiotic Magorrian relation. During phases of overheating,
the hot mode becomes the single channel of accretion (with a different cuspy
temperature profile), though strongly suppressed by turbulence.
