  We present a comparison of the statistical properties of dark matter halo
merger trees extracted from the Millennium Simulation with Extended
Press-Schechter (EPS) formalism and the related GALFORM Monte-Carlo method for
generating ensembles of merger trees. The volume, mass resolution and output
frequency make the Millennium Simulation a unique resource for the study of the
hierarchical growth of structure. We construct the merger trees of present day
friends-of-friends groups and calculate a variety of statistics that quantify
the masses of their progenitors as a function of redshift; accretion rates; and
the redshift distribution of their most recent major merger. We also look in
the forward direction and quantify the present day mass distribution of halos
into which high redshift progenitors of a specific mass become incorporated. We
find that EPS formalism and its Monte-Carlo extension capture the qualitative
behaviour of all these statistics but, as redshift increases they
systematically underestimate the masses of the most massive progenitors. This
shortcoming is worst for the Monte-Carlo algorithm. We present a fitting
function to a scaled version of the progenitor mass distribution and show how
it can be used to make more accurate predictions of both progenitor and final
halo mass distributions.
