  (abridged) We study the mass assembly history (MAH) of dark matter haloes. We
compare MAHs obtained using (i) merger trees constructed with the extended
Press-Schechter (EPS) formalism, (ii) numerical simulations, and (iii) the
Lagrangian perturbation code PINOCCHIO. We show that the PINOCCHIO MAHs are in
excellent agreement with those obtained using numerical simulations. Using a
suite of 55 PINOCCHIO simulations, with 256^3 particles each, we study the MAHs
of 12,924 cold dark matter haloes in a \LambdaCDM concordance cosmology. We
show that haloes less massive than the characteristic non-linear mass scale
establish their potential wells much before they acquire most of their mass.
The time when a halo reaches its maximum virial velocity roughly divides its
mass assembly into two phases, a fast accretion phase which is dominated by
major mergers, and a slow accretion phase dominated by minor mergers. Each halo
experiences about 3 \pm 2 major mergers since its main progenitor had a mass
equal to one percent of the final halo mass. This major merger statistic is
found to be virtually independent of halo mass. However, the average redshift
at which these major mergers occur, is strongly mass dependent, with more
massive haloes experiencing their major mergers later.
