We construct merger trees of dark matter haloes and quantify their merger
rates and mass growth rates using the joint dataset from the Millennium and
Millennium-II simulations. The finer resolution of the Millennium-II Simulation
has allowed us to extend our earlier analysis of halo merger statistics to an
unprecedentedly wide range of descendant halo mass (10^10 < M0 < 10^15 Msun),
progenitor mass ratio (10^-5 < xi < 1), and redshift (0 < z < 15). We update
our earlier fitting form for the mean merger rate per halo as a function of
M_0, xi, and z. The overall behavior of this quantity is unchanged: the rate
per unit redshift is nearly independent of z out to z~15; the dependence on
halo mass is weak (M0^0.13); and it is nearly a power law in the progenitor
mass ratio (xi^-2). We also present a simple and accurate fitting formula for
the mean mass growth rate of haloes as a function of mass and redshift. This
mean rate is 46 Msun/yr for 10^12 Msun haloes at z=0, and it increases with
mass as M^{1.1} and with redshift as (1+z)^2.5 (for z > 1). When the fit for
the mean mass growth rate is integrated over a halo's history, we find
excellent match to the mean mass assembly histories of the simulated haloes. By
combining merger rates and mass assembly histories, we present results for the
number of mergers over a halo's history and the statistics of the redshift of
the last major merger.Comment: 12 pages, 9 figures, accepted in MNRA