Accretion onto supermassive black holes (BHs) from the ISM can occur via capture of cold gas 'clouds' (GMCs, clumps, or overdense structures). Unlike material in stellar tidal disruptions or X-ray binaries, or classical Bondi accretion, ISM clouds are strongly magnetized (plasma β ≡ P_(rm thermal)/P_(rm magnetic) ≪ 1), with supersonic turbulence, and cool rapidly. We derive analytic scalings for the initial conditions of accretion disks formed by capture/disruption of such clouds, in three regimes: (1) low-mass BHs (M_(rm BH) ≪ M_(rm cl)), where turbulent Bondi-Hoyle or hierarchical 'leapfrog' growth via sub-cloud encounters dominates; (2) comparable-mass encounters (M_(rm BH) ∼ M_(rm cl)); and (3) massive BHs tidally disrupting small clouds (M_(rm BH) ≫ M_(rm cl)). In each, the resulting disk is predicted to be initially toroidally-magnetically-dominated (|B_φ| ≫ |B_z|, β ≪ 1), geometrically thick (H/R ∼ 0.1-1), and gravitationally stable (Q ≳ 1), with super-sonic, trans-Alfvenic turbulence. These conditions differ qualitatively from those assumed in classical accretion/α disk theory, 'chaotic cold accretion', stellar tidal disruption, or Bondi-Hoyle accretion. At least initially, the toroidal field should be sustained by flux-freezing on timescales shorter than Parker or turbulent resistive losses. We examine how cloud mass spectra drive accretion rate distributions, duty cycles, and fueling rates, with integrated BH growth dominated by clouds of mass comparable to the BH. Given known cosmological evolution, we suggest a scenario linking (a) inefficient growth and wandering BHs in dwarf galaxies, (b) hyper-Eddington growth in little red dots, (c) peak quasar activity in massive gas-rich systems at cosmic noon, and (d) lower-luminosity AGN in gas-poor galaxies at late times.