  We study the effect of a nearby planar wall on the propulsion of a spherical
phoretic micro-swimmer driven by reactions on its surface. An asymmetric
coverage of catalysts on its surface which absorb reactants and generate
products gives rise to an anisotropic interfacial flow that propels the
swimmer. We analyse the near-wall dynamics of such a self-phoretic swimmer as a
function of the asymmetric catalytic coverage of the surface. By an analysis of
the fundamental singularities of the flow and concentration or electrostatic
potential gradients generated we are able to obtain and rationalise a phase
diagram of behaviours as a function of the characteristics of the swimmer
surface. We find a variety of possible behaviours, from "bound states" where
the swimmer remains near the wall to "scattering" or repulsive trajectories in
which the swimmer ends far from the wall. The formation of some of the bound
states is a purely wall-phoretic effect and cannot be obtained by simply
mapping a phoretic swimmer to a hydrodynamic one.
