The journey of QSO haloes from z=6 to the present
  We apply a recently developed scaling technique to the Millennium-XXL, one of
the largest cosmological N-body simulations carried out to date 3x10^11
particles within a cube of volume ~70Gpc^3). This allows us to investigate the
cosmological parameter dependence of the mass and evolution of haloes in the
extreme high-mass tail of the z=6 distribution. We assume these objects to be
likely hosts for the population of rare but ultraluminous high-redshift quasars
discovered by the Sloan Digital Sky Survey. Haloes with a similar abundance to
these quasars have a median mass of 9x10^12 Msun in the currently preferred
cosmology, but do not evolve into equally extreme objects at z=0. Rather, their
descendants span the full range conventionally assigned to present-day
clusters, 6x10^13 to 2.5x10^15 Msun for this same cosmology. The masses both at
z=6 and at z=0 shift up or down by factors exceeding two if cosmological
parameters are pushed to the boundaries of the range discussed in published
interpretations of data from the WMAP satellite. The main factor determining
the future growth of a high-mass z=6 halo is the mean overdensity of its
environment on scales of 7 to 14 Mpc, and descendant masses can be predicted 6
to 8 times more accurately if this density is known than if it is not. All
these features are not unique to extreme high-z haloes, but are generic to
hierarchical growth. Finally, we find that extreme haloes at z=6 typically
acquired about half of their total mass in the preceding 100 Myr, implying very
large recent accretion rates which may be related to the large black hole
masses and high luminosities of the SDSS quasars.
