  We use the extended Press-Schechter formalism to investigate the rate at
which cold dark matter haloes accrete mass. We discuss the shortcomings of
previous methods that have been used to compute the mass accretion histories of
dark matter haloes, and present an improved method based on the N-branch merger
tree algorithm of Somerville & Kolatt. We show that this method no longer
suffers from inconsistencies in halo formation times, and compare its
predictions with high resolution N-body simulations. Although the overall
agreement is reasonable, there are slight inconsistencies which are most easily
interpreted as a reflection of ellipsoidal collapse (as opposed to spherical
collapse assumed in the Press-Schechter formalism). We show that the average
mass accretion histories follow a simple, universal profile, and we present a
recipe for computing the two scale-parameters which is applicable to a wide
range of halo masses and cosmologies. Together with the universal profiles for
the density and angular momentum distributions of CDM haloes, these universal
mass accretion histories provide a simple but accurate framework for modeling
the structure and formation of dark matter haloes. In particular, they can be
used as a backbone for modeling various aspects of galaxy formation where one
is not interested in the detailed effects of merging. As an example we use the
universal mass accretion history to compute the rate at which haloes accrete
mass, which we compare to the cosmic star formation history of the Universe.
