Bondi theory is often assumed to adequately describe the mode of accretion in astrophysical environments. However, the Bondi flow must be adiabatic, spherically symmetric, steady, unperturbed, with constant boundary conditions. Using 3D adaptive mesh refinement simulations, linking the 50 kpc to the sub-parsec (sub-pc) scales over the course of 40 Myr, we systematically relax the classic assumptions in a typical galaxy hosting a supermassive black hole. In the more 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 non-linear growth of thermal instabilities, leading to the condensation of cold clouds and filaments when t(cool)/t(ff) less than or similar to 10. The clouds decouple from the hot gas, 'raining' on to the centre. Subsonic turbulence of just over 100 km s(-1) (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) less than or similar to 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. In this study, we do not inject a fixed initial angular momentum, though vorticity is later seeded by turbulence. 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 the frequent fluctuations. Since our modelling is fairly general (turbulence/heating due to AGN feedback, galaxy motions, mergers, stellar evolution), chaotic cold accretion may be common in many systems, such as hot galactic haloes, groups and clusters. 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. Chaotic accretion can generate high-velocity clouds, likely leading to strong variations in the AGN luminosity, and the deflection or mass-loading of jets. During phases of overheating, the hot mode becomes the single channel of accretion, though strongly suppressed by turbulence. High-resolution data could determine the current mode of accretion: assuming quiescent feedback, the cold mode results in a quasi-flat-temperature core as opposed to the cuspy profile of the hot mode.
