How big could a black hole get?

There is no theoretical upper limit to the mass of a black hole. However, astronomers have noted that the ultramassive black holes (UMBHs) found in the cores of some galaxies never seem to exceed about 10 billion solar masses. This is exactly what we’d expect from the rate at which we know black holes grow, given the time that’s elapsed since the Big Bang. Furthermore, recent studies suggest that UMBHs cannot physically grow much beyond this anyway, since they would then begin to disrupt the accretion discs that feed them, choking the source of new material.