The largest observed supermassive black holes (SMBHs) have a mass of M_BH ~ 10^{10} M_sun, nearly independent of redshift, from the local (z~0) to the early (z>6) Universe. We suggest that the growth of SMBHs above a few 10^{10} M_sun is prevented by small-scale accretion physics, independent of the properties of their host galaxies or of cosmology. Growing more massive BHs requires a gas supply rate from galactic scales onto a nuclear region as high as >10^3 M_sun/yr. At such a high accretion rate, most of the gas converts to stars at large radii (~10-100 pc), well before reaching the BH. We adopt a simple model (Thompson et al. 2005) for a star-forming accretion disk, and find that the accretion rate in the sub-pc nuclear region is reduced to the smaller value of at most a few M_sun/yr. This prevents SMBHs from growing above ~10^{11} M_sun in the age of the Universe. Furthermore, once a SMBH reaches a sufficiently high mass, this rate falls below the critical value at which the accretion flow becomes advection dominated. Once this transition occurs, BH feeding can be suppressed by strong outflows and jets from hot gas near the BH. We find that the maximum SMBH mass, given by this transition, is between M_{BH,max} ~ (1-6) * 10^{10} M_sun, depending primarily on the efficiency of angular momentum transfer inside the galactic disk, and not on other properties of the host galaxy.
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