  The use of parallel computers and increasingly sophisticated software has
allowed us to perform a large suite of N-body simulations using from $10^8$,to
$10^9$ particles. We will report on our recent convergence tests of the halo
mass function, N-point correlation functions, power spectrum and pairwise
velocity from very large high resolution treecode N-body simulations. Rather
than basing results on just one or two large simulations, now one can
investigate the role of different numerical and physical effects on the
statistics used to characterize the mass distribution of the Universe.
