In a recent paper we measured the lateral hole diffusion in a GaAs/AlGaAs single quantum well (SQW) by a novel method. At helium temperature, we estimate a lateral hole diffusion length in the QW of 1.5 mum. However, the assumption that diffusion takes place mainly in the, SQW needs to be checked, as the measured diffusion length is the result of two competing processes: (i) hole diffusion in the SQW plane itself and (ii) hole diffusion in the barrier followed by recombination in the SQW. We present here a comparison between the lateral hole distribution in the SQW and in the AlGaAs barrier. First, we estimate the hole diffusion length in the barrier fitting experimental cathodoluminescence linescans on simulated ones. Second, using the measured diffusion lengths in the QW plane and in the bulk barrier and modeling the carrier transport, we deduce the lateral hole distribution in both layers. It is found that even for very large barriers (1.2 mum), the hole diffusion in the barrier contributes less than 0.1% of the total lateral hole diffusion. The lateral transport is mainly carried by holes in the QW (2D diffusion) due to their confinement in the well.