Polymer molecules densely tethered to surfaces (polymer brushes) can improve the colloidal stability of dispersion by protecting particles against aggregation. We use mean field and self-consistent field theoretical models to consider repulsive interactions between brushes of branched (dendritic) macromolecules tethered to planar and spherical surfaces. It is demonstrated that compared to planar brushes of linear chains, the brushes composed of dendritic macromolecules provide a sharper repulsive force when pushed to overlap. The sharp increase in force is found also for dendron brush-decorated spherical particles. At the same distance between surfaces, apposing dendron brushes interpenetrate less than brushes of linear chains with the same mass per unit area. Hence the colloidal stability of dendron brush-decorated particles will go hand in hand with g improved tribological properties of dispersions.