The recent discoveries of luminous quasars at high redshifts imply that black holes more massive than a few billion solar masses have been assembled already when the universe was less than a billion years old .
We show that the existence of these black holes is not surprising in popular hierarchical models of structure formation .
For example , the black hole needed to power the quasar SDSS 1044-0125 at z = 5.8 can arise naturally from the growth of stellar-mass seeds forming at z > 10 , when typical values are assumed for the radiative accretion efficiency ( \sim 0.1 ) , and the bolometric accretion luminosity in Eddington units ( \sim 1 ) .
Nevertheless , SDSS 1044-0125 yields a non–trivial constraint on a combination of these parameters .
Extrapolating our model to future surveys , we derive the highest plausible redshift for quasars which are not lensed or beamed , as a function of their apparent magnitude .
We find that at a limiting magnitude of K \sim 20 , quasar surveys can yield strong constraints on the growth of supermassive black holes out to z \sim 10 .