Roughness and Nonlinearities in (2 + 1)-Dimensional Growth Models with Diffusion

We present results of numerical simulations of kinetic roughening for three variants of a growth model with surface diffusion in 2 + 1 dimensions. The variants differ by the rules of relaxation of a freshly arrived particle giving different effective roughness and dynamical exponents. In particular we have found that the model, studied by Wolf and Villain and by Das Sarma and Tamborenea in 1 + 1 dimensions, has in 2 + 1 dimensions exponents corresponding to a nonlinear differential equations.