We apply a recently developed scaling technique to the Millennium-XXL, one of the largest cosmological N-body simulations carried out to date (3 × 1011 particles within a cube of volume ∼70 Gpc3). 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 (SDSS). Haloes with a similar abundance to these quasars have a median mass of 9 × 1012 M⊙ 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, 6 × 1013–2.5 × 1015 M⊙ for the same cosmology. The masses both at z = 6 and at z = 0 shift up or down by factors exceeding 2 if cosmological parameters are pushed to the boundaries of the range discussed in published interpretations of data from the Wilkinson Microwave Anisotropy Probe 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 7–14 Mpc, and descendant masses can be predicted six to eight 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 acquire 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.