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Using analytical and numerical self-consistent field (SCF) methods we analyze equilibrium structure of dry (solvent-free) brush of branched polymers in wide range of chain grafting densities. A detailed analysis is performed for starlike polymers end-tethered to planar surface by terminal monomer of one of their branches. At moderate grafting densities ensuring Gaussian elasticity of tethered stars the brush structure is described by strong stretching SS-SCF theory employing parabolic molecular potential. At high grafting densities an approximate analytical AA-SCF theory is used to describe stratification of dry brush. Analytical predictions are supplemented by results of numerical Scheutjens-Fleer SF-SCF model. Interpenetration between dry brushes is analyzed as a function of grafting density and degree of branching of tethered chains. Comparison of interpenetration and friction between dry brushes with varied chain architectures pointed at optimal lubrication by macrocycles tethered to the surface by branching point. It is demonstrated that shear stress in sliding brushes of starlike macromolecules sharply decreases at high grafting densities corresponding to almost full stretching of the longest elastic path in the polymers. [ABSTRACT FROM AUTHOR]