We have investigated lateral transport mechanisms in epitaxial lateral overgrowth (ELO) of GaN grown by Metal organic chemical vapor deposition (MOCVD). Portions of a pre-grown GaN buffer layer are patterned with a dielectric mask material, silicon nitride. Further growth of GaN occurs selectively on exposed areas of the underlying buffer layer, and not on the dielectric material. Growth-rate enhancement on the exposed GaN is observed due to lateral transport of material from the masked regions. We describe experiments to distinguish whether the lateral transport of material occurs via gas-phase diffusion or surface diffusion, either on the mask itself or on the epitaxial material. Deep trenches were etched into the wafer prior to the ELO growth, designed to interrupt lateral transport if it were occurring by diffusion along the surface. ELO growth rate profiles on exposed line patterns and on larger area blanket growth zones were examined with and without the trenches. Growth profiles were virtually identical independent of the presence of the trench features. These results indicate that gas-phase diffusion dominates the transport of material during GaN ELO.