An exponentially accelerated convergent growth scheme for the synthesis of dendritic macromolecules is described and demonstrated. By this process, the number of repeat units per dendrimer accumulates according to a double exponential function in terms of generation, n. The process employs a single trifunctional monomer of the type A(p)(B-p)(2) having orthogonally protected functional groups. The repetitive process involves selective removal of the protecting groups on A(p) in one portion, selective removal of the protecting groups on B-p in a second portion, and subsequent coupling of the two monoprotected intermediates in a proper stoichiometric ratio. The new monodendron maintains a single A(p) group at its focal point but contains x(2)B(p) peripheral groups where x is the number of peripheral groups in the preceding generation. The double exponential growth scheme is demonstrated by the synthesis of a third-generation (255-mer) phenylacetylene monodendron that is characterized by ultraviolet matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (calculated molecular weight 39.972 kDa, observed m/z 39.969 kDa).