  We study the growth of the genus zero Gromov-Witten invariants GW_{nD} of the
projective plane P^2_k blown up at k points (where D is a class in the second
homology group of P^2_k). We prove that, under some natural restrictions on D,
the sequence log GW_{nD} is equivalent to lambda n log n, where lambda =
D.c_1(P^2_k).
