The aim is a quantitative determination of the effective pair-potentials between droplets within Pickering emulsions of (oil-in-water or water-in-oil types), which are protected by end-grafted polymer-chains via (uncharged) big solid particles. This strong and irreversible grafting mode plays a fundamental role and rends the emulsions more stable, even in the absence of the charges. The droplets stabilization is very sensitive to the bath temperature that controls the solvent quality, the number of grafted-polymers per droplet (or grafting-density), and the concentration of monomers that float in the continuous phase (water or oil). The effective interaction between the hairy-droplets is a sum of two parts: the steric interaction coming from the excluded-volume forces, and the second is simply the usual van der Waals attraction. First, taking advantage of those results already derived using Renormalization Theory techniques, we determine the expression of the repulsive part of the overall pair-potentials, for all distances between the interacting hairy-droplets. Second, we study all the analytic properties of the obtained overall pair-potential, taking into account the solvent quality, the values of the bulk monomer concentration and the grafting-density. Third, these analytic properties enable us to classify the various shapes of the pair-potentials in space of the pertinent parameters. In particular, in any case (good and theta-solvents), we observe that, for high-grafting-densities (above some known critical value) or small monomer concentration (below some known critical value), the potentials exhibit an energy barrier that prevents the coalescence of the hairy-droplets. As remark, incidentally, the determined expressions of the pair-potentials are very similar to those of the DLVO potentials. Fourth, we draw the architectures of the phase diagrams in the (N,f)-plan, for dilute solutions, and in (f,Φ0)-plan, for semi-dilute solutions, where N, f and Φ0 denote the polymerization degree of the grafted-polymer-chains, their number per hairy-droplet and the monomer volume fraction, respectively. Finally, we discuss a link of the present work to experiment.