We present cosmological hydrodynamic simulations of a quasar-mass halo ($M_{rm halo} approx 10^{12.5},{rm M}_{odot}$ at z=2) that for the first time resolve gas transport down to the inner 0.1 pc surrounding the central massive black hole. We model a multi-phase interstellar medium including stellar feedback by supernovae, stellar winds, and radiation, and a hyper-Lagrangian refinement technique increasing the resolution dynamically approaching the black hole. We do not include black hole feedback. We show that the sub-pc inflow rate (1) can reach ~6 M$_{odot}$yr$^{-1}$ roughly in steady state during the epoch of peak nuclear gas density (z~2), sufficient to power a luminous quasar, (2) is highly time variable in the pre-quasar phase, spanning 0.001-10 M$_{odot}$yr$^{-1}$ on Myr timescales, and (3) is limited to short (~2 Myr) active phases (0.01-0.1 M$_{odot}$yr$^{-1}$) followed by longer periods of inactivity at lower nuclear gas density and late times (z~1), owing to the formation of a hot central cavity. Inflowing gas is primarily cool, rotational support dominates over turbulence and thermal pressure, and star formation can consume as much gas as provided by inflows across 1 pc - 10 kpc. Gravitational torques from multi-scale stellar non-axisymmetries dominate angular momentum transport over gas self-torquing and pressure gradients, with accretion weakly dependent on black hole mass. Sub-pc inflow rates correlate with nuclear (but decouple from global) star formation and can exceed the Eddington rate by x10. The black hole can move ~10 pc from the galaxy center on ~0.1 Myr. Accreting gas forms pc-scale, rotationally supported, obscuring structures often misaligned with the galaxy-scale disk. These simulations open a new avenue to investigate black hole-galaxy co-evolution.
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