  The influence of the initial fluctuations on the onset of scaling in the
quench to zero temperature of a two dimensional system with conserved order
parameter, is analyzed in detail with and without topological defects. We find
that the initial fluctuations greatly affect the way scaling is reached, while
the number of components of the order parameter does not play a significant
role. Under strong initial fluctuations the preasymptotic linear behavior is
replaced by the mean field behavior of the large-N model, producing the
multiscaling to standard-scaling crossover also in the physically interesting
cases of systems with a small number of components.
