N-body simulations are employed to investigate relationships between the global properties of collisionless, self-gravitating systems (e.g., galaxies) that result from hierarchical merging. Each galaxy of mass M is assumed to form by the merging of two identical progenitors of mass 1/2 M from an interpenetrating parabolic encounter. A power-law relation between galaxy mass and central velocity dispersion results, with exponent similar to the observed luminosity-velocity dispersion relation for ellipticals. Since this relation appears to be entirely scale-free, the authors inspect observational data on other stellar systems supported primarily by random motion (globular clusters and dwarf elliptical galaxies). The possibility that hierarchical merging has operated over many decades in mass is discussed.