  We make black hole (BH) merger trees from Millennium and Millennium-II
simulations to find under what conditions 10^9Msun SMBH can form by redshift
z=7. In order to exploit both: large box size in the Millennium simulation; and
large mass resolution in the Millennium-II simulation, we develop a method to
combine these two simulations together, and use the Millennium-II merger trees
to predict the BH seeds to be used in the Millennium merger trees. We run
multiple semi-analytical simulations where SMBHs grow through mergers and
episodes of gas accretion triggered by major mergers. As a constraint, we use
observed BH mass function at redshift z=6. We find that in the light of the
recent observations of moderate super-Eddington accretion, low-mass seeds
(100Msun) could be the progenitors of high-redshift SMBHs (z~7), as long as the
accretion during the accretion episodes is moderately super-Eddington, where
f_Edd=3.7 is the effective Eddington ratio averaged over 50 Myr.
