  We study merger histories of dark-matter haloes in a suite of N-body
simulations that span different cosmological models. The simulated cases
include the up-to-date WMAP5 cosmology and other test cases based on the
Einstein-deSitter cosmology with different power spectra. We provide a robust
fitting function for the conditional mass function (CMF) of progenitor haloes
of a given halo. This fit is valid for the different cosmological models and
for different halo masses and redshifts, and it is a significant improvement
over earlier estimates. Based on this fit, we develop a simple and accurate
technique for transforming the merger history of a given simulated halo into
haloes of different mass, redshift and cosmology. Other statistics such as
main-progenitor history and merger rates are accurately transformed as well.
This method can serve as a useful tool for studying galaxy formation. It is
less sensitive to the low accuracy of the fit at small time-steps, and it can
thus replace the more elaborate task of construction Monte-Carlo realizations.
As an alternative approach, we confirm the earlier finding by Neistein & Dekel
that the main-progenitor follows a log-normal distribution. This property of
merger trees allows us to better capture their behaviour as a function of time
and descendant mass, but a broader suite of simulations is required for
evaluating the dependence of the log-normal parameters on the cosmological
model.
