We present a theory of conformational transition triggered by inferior solvent strength in brushes formed by dendritically branched macromolecules tethered to planar, concave, or convex cylindrical and spherical surfaces. In the regime of linear elasticity for brush-forming dendrons, an analytical strong stretching self-consistent field (SS-SCF) approach provides brush conformational properties as a function of solvent strength. A boxlike model is applied to describe the collapse transition in brushes formed by macromolecules with arbitrary treelike topology, including hyperbranched polymers. We demonstrate that an increase in the degree of branching, that is, an increase in the number of generations or/and functionality of branching points in tethered macromolecules, makes the swelling-to-collapse transition less sharp. A decrease in surface curvature has a similar effect. The numerical Scheutjens-Fleer self consistent field approach is used to analyze the collapse transition in dendron brushes in the nonlinear stretching regime. It is demonstrated that inferior solvent strength suppresses stratification that is exhibited under good solvent conditions by densely grafted dendron brushes.