In p+ GaAs thin films, the effect of photoelectron degeneracy on spin transport is investigated theoretically and experimentally by imaging the spin polarization profile as a function of distance from a tightly focused light excitation spot. Under degeneracy of the electron gas (high concentration, low temperature), a dip at the center of the polarization profile appears with a polarization maximum at a distance of about 2μm from the center. This counterintuitive result reveals that photoelectron diffusion depends on spin, as a direct consequence of the Pauli principle. This causes a concentration dependence of the spin stiffness while the spin dependence of the mobility is found to be weak in doped material. The various effects which can modify spin transport in a degenerate electron gas under local laser excitation are considered. A comparison of the data with a numerical solution of the coupled diffusion equations reveals that ambipolar coupling with holes increases the steady-state photoelectron density at the excitation spot and therefore the amplitude of the degeneracy-induced polarization dip. Thermoelectric currents are predicted to depend on spin under degeneracy (spin Soret currents), but these currents are negligible except at very high excitation power where they play a relatively small role. Coulomb spin drag and band-gap renormalization are negligible due to electrostatic screening by the hole gas.