We investigate the asymptotic behaviour, as e → 0, of a class of monotone nonlinear Neumann problems, with growth p -1 (p ∈]1, +∞[), on a bounded multidomain (N ≥ 2). The multidomain ΩE is composed of two domains. The first one is a plate which becomes asymptotically flat, with thickness hE in the x N direction, as e → 0. The second one is a “forest of cylinders distributed with e -periodicity in the first N - 1 directions on the upper side of the plate. Each cylinder has a small cross section of size e and fixed height (for the case N=3 , see the figure). We identify the limit problem, under the assumption: . After rescaling the equation, with respect to hE , on the plate, we prove that, in the limit domain corresponding to the “forest of cylinders, the limit problem identifies with a diffusion operator with respect to x N , coupled with an algebraic system. Moreover, the limit solution is independent of x N in the rescaled plate and meets a Dirichlet transmission condition between the limit domain of the “forest of cylinders and the upper boundary of the plate.