Accretion History of Subhalo Population now and then
  In the standard model of structure formation galaxies reside in virialized
dark matter haloes which extend much beyond the observational radius of the
central system. The dark matter halo formation process is hierarchical, small
systems collapse at high redshift and then merge together forming larger ones.
In this work we study the mass assembly history of host haloes at different
observation redshifts and the mass function of accreted satellites (haloes that
merge directly on the main halo progenitor). We show that the satellite mass
function is universal, both independent on the host halo mass and observation
redshift. The satellite mass function also turn out to be universal once only
satellites before or after the host halo formation redshift (time at which the
main halo progenitor assembles half of its final mass) are considered. We show
that the normalizations of these distributions are directly related to the main
halo progenitor mass distributions before and after its formation, while their
slope and the exponential high mass cut-off remain unchanged.
