A diffusive theory of random lasing is derived for finite systems comprised of disordered arrays of laser active
ZnO nanopillars. The diffusive transport of the light intensity is coupled to the semiclassical laser rate equations,
therefore incorporating nonlinear optical gain in this effectively two dimensional system. We solve the resulting
boundary condition problem to obtain the full spatial intensity profile of lasing spots in dependence of the pumprate
and other system parameters. Our theory predicts two different types of random laser modes in effectively
two dimensional systems in general. A surface mode with a large size extending over the entire sample width,
and a bulk mode, with small laser spot sizes. We discuss their origin and characteristics.