The lubrication with oil-in-water emulsions is usually supposed to be governed by the oil phase being concentrated in a reservoir that supplies the contact. In this paper, another lubrication process in an elastohydrodynamic ball/disc contact is presented. It is found that above a critical entrainment speed a thick film grows in the contact with time and reaches a limiting thickness. Viscous adherent boundary layers are formed and observed on both the surfaces. Pressure and speed are required for the film build-up, An additional sliding speed at constant entrainment speed induces a shearing at the interface between the boundary layers and the substrate that depends oil the nature of the contacting surface, It is shown that these high viscosity, boundary films ensure a starved lubrication. The modelling of the starvation process allows its to evaluate the viscosity of these boundary layers and their mean supply rate to the contact. A fine analysis of this latter parameter shows that the lubricating film results from the equilibrium between the flow rate of lubricating particles in the inlet zone and the amount of particles that cannot stay, in the contact between two passages which strongly depends oil the entrainment speed. A classical adsorption process does not seem responsible for the anchorage of the boundary films to the surfaces. The adherence of the films is explained by an approach based on electric interactions between ionic surfactants anti the oxidized metallic surfaces according to the position of their isoelectric point compared to the pH of the emulsion.