  In this paper we study the steady state of the fluctuations of the surface
for a model of surface growth with relaxation to any of its lower nearest
neighbors (SRAM) [F. Family, J. Phys. A {\bf 19}, L441 (1986)] in scale free
networks. It is known that for Euclidean lattices this model belongs to the
same universality class as the model of surface relaxation to the minimum
(SRM). For the SRM model, it was found that for scale free networks with
broadness $\lambda$, the steady state of the fluctuations scales with the
system size $N$ as a constant for $\lambda \geq 3$ and has a logarithmic
divergence for $\lambda < 3$ [Pastore y Piontti {\it et al.}, Phys. Rev. E {\bf
76}, 046117 (2007)]. It was also shown [La Rocca {\it et al.}, Phys. Rev. E
{\bf 77}, 046120 (2008)] that this logarithmic divergence is due to non-linear
terms that arises from the topology of the network. In this paper we show that
the fluctuations for the SRAM model scale as in the SRM model. We also derive
analytically the evolution equation for this model for any kind of complex
graphs and find that, as in the SRM model, non-linear terms appear due to the
heterogeneity and the lack of symmetry of the network. In spite of that, the
two models have the same scaling, but the SRM model is more efficient to
synchronize systems.
