  In a previous paper, we described a new method for including detailed
information about substructure in semi-analytic models of dark matter halo
formation based on merger trees. In this paper, we present the basic
predictions of our full model of halo formation. We first describe the overall
properties of substructure in galaxy, group or cluster haloes at the present
day. We then discuss the evolution of substructure, and the effect of the mass
accretion history of an individual halo on the mass function and orbital
grouping of its subhalo population. We show, in particular, that the shape of
the subhalo mass function is strongly correlated with the formation epoch of
the halo. In a third paper in this series we will compare the results of our
semi-analytic method with the results of self-consistent numerical simulations
of halo formation.

Astrophysics