  We systematically study the effects of varying the starting redshift z_i for
cosmological simulations in the highly non-linear regime. Our primary focus
lies with the (individual) properties of dark matter halos -- namely the mass,
spin, triaxiality, and concentration -- where we find that even substantial
variations in z_i leave only a small imprint, at least for the probed mass
range M \in [10^{10}, 10^{13}] Msun/h and when investigated at redshift z=0. We
further compare simulations started by using the standard Zel'dovich
approximation to runs based upon initial conditions produced with second order
Lagrangian perturbation theory. Here we observe the same phenomenon, i.e. that
differences in the studied (internal) properties of dark matter haloes are
practically undetectable. These findings are (for the probed mass range) in
agreement with other work in the literature. We therefore conclude that the
commonly used technique for setting up cosmological simulations leads to stable
results at redshift z=0 for the mass, the spin parameter, the triaxiality, and
the concentration of dark matter haloes.
