We consider the discrete surface growth process with relaxation to the minimum [F. Family, J. Phys. A {bf 19} L441, (1986).] as a possible synchronization mechanism on scale-free networks, characterized by a degree distribution $P(k) sim k^{-lambda}$
, where $k$ is the degree of a node and $lambda$ his broadness, and compare it with the usually applied Edward-Wilkinson process [S. F. Edwards and D. R. Wilkinson, Proc. R. Soc. London Ser. A {bf 381},17 (1982) ]. In spite of both processes belong to the same universality class for Euclidean lattices, in this work we demonstrate that for scale-free networks with exponents $lambda<3$ this is not true. Moreover, we show that for these ubiquitous cases the Edward-Wilkinson process enhances spontaneously the synchronization when the system size is increased, which is a non-physical result. Contrarily, the discrete surface growth process do not present this flaw and is applicable for every $lambda$.
