Abstract The plasma haloes filling massive galaxies, groups and clusters are shaped by active galactic nucleus (AGN) heating and subsonic turbulence (σ v  ∼ 150 km s−1), as probed by Hitomi. Novel 3D high-resolution simulations show the soft X-ray, keV hot plasma cools rapidly via radiative emission at the high-density interface of the turbulent eddies, stimulating a top-down condensation cascade of warm 104 K filaments. The kpc-scale ionized (optical/ultraviolet) filaments form a skin enveloping the neutral filaments (optical/infrared/21 cm). The peaks of the warm filaments further condense into cold molecular clouds (<50 K; radio) with total mass of several 107 M⊙ and inheriting the turbulent kinematics. In the core, the clouds collide inelastically, mixing angular momentum and leading to Chaotic Cold Accretion (CCA). The black hole accretion rate (BHAR) can be modelled via quasi-spherical viscous accretion, $\dot{M}_\bullet \propto \nu _{\rm c}$ , with clump collisional viscosity νc ≡ λc σ v and λc ∼ 100 pc. Beyond the core, pressure torques shape the angular momentum transport. In CCA, the BHAR is recurrently boosted up to 2 dex compared with the disc evolution, which arises as turbulence becomes subdominant. With negligible rotation too, compressional heating inhibits the molecular phase. The CCA BHAR distribution is lognormal with pink noise, f −1 power spectrum characteristic of fractal phenomena. Such chaotic fluctuations can explain the rapid luminosity variability of AGN and high-mass X-ray binaries. An improved criterium to trace non-linear condensation is proposed: σ v /v cool ≲ 1. The three-phase CCA reproduces key observations of cospatial multiphase gas in massive galaxies, including Chandra X-ray images, SOAR Hα filaments and kinematics, Herschel C+ emission and ALMA molecular associations. CCA plays important role in AGN feedback and unification, the evolution of BHs, galaxies and clusters.