  The structural properties of polydisperse hard spheres in the presence of a
hard wall are investigated via Monte Carlo simulation and density functional
theory (DFT). Attention is focussed on the local density distribution
$\rho(\sigma,z)$, measuring the number density of particles of diameter
$\sigma$ at a distance $z$ from the wall. The form of $\rho(\sigma,z)$ is
obtained for bulk volume fractions $\eta_b=0.2$ and $\eta_b=0.4$ for two
choices of the bulk parent distribution: a top-hat form, which we study for
degrees of polydispersity $\delta=11.5%$ and $\delta=40.4%$, and a truncated
Schulz form having $\delta=40.7%$. Excellent overall agreement is found between
the DFT and simulation results, particularly at $\eta_b=0.2$. A detailed
analysis of $\rho(\sigma,z)$ confirms the presence of oscillatory size
segregation effects observed in a previous DFT study (Pagonabarraga {\em et
al.}, Phys. Rev. Lett. {\bf 84}, 911 (2000)). For large $\delta$, the character
of these oscillation is observed to depend strongly on the shape of the parent
distribution. In the vicinity of the wall, attractive $\sigma$-dependent
depletion interactions are found to greatly enhance the density of the largest
particles. The local degree of polydispersity $\delta(z)$ is suppressed in this
region, while further from the wall it exhibits oscillations.
