  In hierarchical models, the time derivative of the halo mass function may be
thought of as the difference of two terms - a creation term, which describes
the increase in the number of haloes of mass m from mergers of less massive
objects, and a destruction term, which describes the decrease in the number of
m-haloes as these merge with other haloes, creating more massive haloes as a
result. In models where haloes form from a spherical collapse, the distribution
of halo creation times can be estimated from the same formalism which is used
to estimate halo abundances: the constant-barrier excursion-set approach. In
the excursion set approach, moving, rather than constant-barriers, are
necessary for estimating halo abundances when the collapse is triaxial. We show
how the corresponding estimates are modified by providing analytic estimates of
the creation rate for a wide range of halo masses. We then show that these
moving-barrier based predictions are in better agreement with measurements in
numerical simulations than are the corresponding predictions of the spherical
collapse model. These results should be useful for studies of merger-driven
star-formation rates and AGN activity. We also present a similar study of
creation of haloes conditioned on belonging to an object of a certain mass
today, and reach similar conclusions - the moving barrier based estimates are
in substantially better agreement with the simulations. This part of the study
may be useful for understanding the tendency for the oldest stars to exist in
the most massive objects.
