We investigate the evolution over time of the space profiles of precursor films spreading away from a droplet of polymer in the poorly explored pseudo-partial wetting case. We use polystyrene melt droplets on oxidized silicon wafers. Interestingly, the film thicknesses measured by ellispometric microscopy are found in the 0.01 to 1 nm range. These thicknesses were validated by atomic force microscopy measurements performed on the textured film obtained after quenching at room temperature. From this, an effective thickness is obtained and compares well to the thicknesses measured by ellipsometry, validating the use of an optical method in this range of thickness. Ellipsometric microscopy provides a height resolution below the angstrom with lateral resolution, image size, and framerate well adapted to spreading precursor films. From this, we demonstrate that precursor films of polystyrene consist of polymer chains with a surface density decreasing to zero away from the droplet. We further find that the polymer chains follow a simple diffusive law with the diffusion coefficient independent of density. This demonstrates that polystyrene chains spread independently in precursor films in pseudo-partial wetting condition. This behavior differs significantly from the case of chains spreading in total wetting for which the diffusion coefficient was found in the literature to depend on surface density or thickness.