Monte Carlo calculations on model dendrimers demonstrate that individual branches (’dendrons’) of an isolated dendrimer spontaneously demix and are well segregated at equilibrium even when they are chemically identical. This is a result of the particular architecture of this class of macromolecules. It is conjectured that this segregation effect will disappear under high density conditions, e.g. in poor solvents, or at the highest attainable generation number, or in neat fluids of dendrimers. The dendrimers possess fractal self-similarity over a rather narrow scale of lengths with fractal dimensions of the order of 2.4 to 2.8.