  We study the impactor flux and cratering on Ceres and Vesta caused by the
collisional and dynamical evolution of the asteroid Main Belt. We develop a
statistical code based on a well-tested model for the simultaneous evolution of
the Main Belt and NEA size distributions. This code includes catastrophic
collisions and noncollisional removal processes such as the Yarkovsky effect
and the orbital resonances. The model assumes that the dynamical depletion of
the early Main Belt was very strong, and owing to that, most Main Belt
comminution occurred when its dynamical structure was similar to the present
one. Our results indicate that the number of D > 1 km Main Belt asteroids
striking Ceres and Vesta over the Solar System history are approximately 4 600
and 1 100 respectively. The largest Main Belt asteroids expected to have
impacted Ceres and Vesta had diameters of 71.7 km and 21.1 km. The number of D
> 0.1 km craters on Ceres is \sim 3.4 \times 10^8 and 6.2 \times 10^7 on Vesta.
The number of craters with D > 100 km are 47 on Ceres and 8 on Vesta. Our study
indicates that the D = 460 km crater observed on Vesta had to be formed by the
impact of a D \sim 66.2 km projectile, which has a probability of occurr \sim
30% over the Solar System history. If significant discrepancies between our
results about the cratering on Ceres and Vesta and data obtained from the Dawn
Mission were found, they should be linked to a higher degree of collisional
evolution during the early Main Belt and/or the existence of the late heavy
bombardment. An increase in the collisional activity in the early phase may be
provided for an initial configuration of the giant planets consistent with, for
example, the Nice model. From this, the Dawn Mission would be able to give us
clues about the initial configuration of the early Solar System and its
subsequent dynamical evolution.
