  We follow the dynamics of nonlinear waves in two-dimensional disordered
lattices with tunable nonlinearity. In the absence of nonlinear terms Anderson
localization traps the packet in space. For the nonlinear case a destruction of
Anderson localization is found. The packet spreads subdiffusively, and its
second moment grows in time asymptotically as $t^\alpha$. We perform fine
statistical averaging and test theoretical predictions for $\alpha$. Along with
a precise confirmation of the predictions in [Chemical Physics \textbf{375},
548 (2010)], we also find potentially long lasting intermediate deviations due
to a growing number of surface resonances of the wave packet.
