  We use giga-particle N-body simulations to study galaxy cluster populations
in Hubble Volumes of LCDM (Omega_m=0.3, Omega_Lambda=0.7) and tCDM (Omega_m=1)
world models. Mapping past light-cones of locations in the computational space,
we create mock sky surveys of dark matter structure to z~1.4 over 10,000 sq deg
and to z~0.5 over two full spheres. Calibrating the Jenkins mass function at
z=0 with samples of ~1.5 million clusters, we show that the fit describes the
sky survey counts to <~20% acccuracy over all redshifts for systems larger than
poor groups (M>5e13 Msun/h). Fitting the observed local temperature function
determines the ratio beta of specific thermal energies in dark matter and
intracluster gas. We derive a scaling with power spectrum normalization beta
\propto sigma8^{5/3}, and measure a 4% error on sigma8 arising from cosmic
variance in temperature-limited cluster samples. Considering distant clusters,
the LCDM model matches EMSS and RDCS X-ray-selected survey observations under
economical assumptions for intracluster gas evolution. Using transformations of
mass-limited cluster samples that mimic sigma8 variation, we explore SZ search
expectations for a 10 sq deg survey complete above 10^{14} Msun/h. Cluster
counts are shown to be extremely sensitive to sigma8 uncertainty while redshift
statistics, such as the sample median, are much more stable. For LCDM, the
characteristic temperature at fixed sky surface density is a weak function of
redshift, implying an abundance of hot clusters at z>1. Assuming constant beta,
four kT>8 keV clusters lie at z>2 and 40 kT>5 keV clusters lie at z>3 on the
whole sky. Detection of Coma-sized clusters at z>1 violate LCDM at 95%
confidence if their surface density exceeds 0.003 per sq deg, or 120 on the
whole sky.
