Observations suggest that a large fraction of black hole growth occurs in normal star-forming disk galaxies .
Here we describe simulations of black hole accretion in isolated disk galaxies with sufficient resolution ( \sim 5 pc ) to track the formation of giant molecular clouds that feed the black hole .
Black holes in z \sim 2 gas-rich disks ( f _ { gas } \approx 50 % ) occasionally undergo \sim 10 Myr episodes of Eddington-limited accretion driven by stochastic collisions with massive , dense clouds .
We predict that these gas-rich disks host weak AGNs \sim 1 / 4 of the time , and moderate/strong AGNs \sim 10 % of the time .
Averaged over \sim 100 Myr timescales and the full distribution of accretion rates , the black holes grow at a few per cent of the Eddington limit – sufficient to match observations and keep the galaxies on the M _ { BH } - M _ { bulge } relation .
This suggests that dense cloud accretion in isolated z \approx 2 disks could dominate cosmic black hole growth .
In z \sim 0 disks with f _ { gas } \approx 10 % , Eddington-limited growth is extremely rare because typical gas clouds are smaller and more susceptible to disruption by AGN feedback .
This results in an average black hole growth rate in high- f _ { gas } galaxies that is up to 10 ^ { 3 } times higher than that in low- f _ { gas } galaxies .
In all our simulations , accretion shows variability by factors of \sim 10 ^ { 4 } on a variety of time scales , with variability at \sim 1 Myr scales driven by the structure of the interstellar medium .