We show that Random Branching Theory (RBT) accurately describes the structures of various synthetic and natural highly branched polymers in solution. We test the theory against data taken from the literature, including radii of gyration of glycogen, hyperbranched polyglycerols, and polyamidoamine dendrimers and the small-angle X-ray scattering profiles of these same dendrimers. In particular, all these polymers can be described adequately by sequentially branching units, packed together in a random close packing arrangement. Combined with previous tests against experiments and computer simulations, the evidence presented here shows that RBT is a simple, but surprisingly useful, theory of highly branched polymers' solution structure. We suggest that it is sufficiently powerful to be useful in the design of new polymers. Our most surprising conclusion is that random attachment of component parts produces a good model of regularly branched polymers. (C) 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1525-1538, 2011