  Synchronization problems in complex networks are very often studied by
researchers due to its many applications to various fields such as
neurobiology, e-commerce and completion of tasks. In particular, Scale Free
networks with degree distribution $P(k)\sim k^{-\lambda}$, are widely used in
research since they are ubiquitous in nature and other real systems. In this
paper we focus on the surface relaxation growth model in Scale Free networks
with $2.5< \lambda <3$, and study the scaling behavior of the fluctuations, in
the steady state, with the system size $N$. We find a novel behavior of the
fluctuations characterized by a crossover between two regimes at a value of
$N=N^*$ that depends on $\lambda$: a logarithmic regime, found in previous
research, and a constant regime. We propose a function that describes this
crossover, which is in very good agreement with the simulations. We also find
that, for a system size above $N^{*}$, the fluctuations decrease with
$\lambda$, which means that the synchronization of the system improves as
$\lambda$ increases. We explain this crossover analyzing the role of the
network's heterogeneity produced by the system size $N$ and the exponent of the
degree distribution.
