The Rouse-Zimm discrete hydrodynamic model is extended to acyclic macromolecules of any topology, and particular attention is devoted to starlike dendrimers and other symmetric cascade structures. As a first approximation freely rotating models are built for branched structures by means of appropriate choices of topology-dependent stiffness parameters. Relevant dynamic observables (depending on the spectrum of viscoelastic relaxation rates) are studied as functions of local stiffness, of branching topology, and of dendrimer generational growth. The present results show that a moderate increase of local stiffness accounts for the molecular dimensions of dendrimers as previously calculated by Mansfield and Klushin [J. Phys. Chem. 96, 3994 (1992)] by Monte Carlo methods, and reproduces with good precision their results for the intrinsic viscosity (upper-bound calculations). Thus omission of excluded-volume interactions within the present models can be at least partially compensated for by suitable choices of local stiffness parameters, provided than the chain portions between branching points are not very long. In addition, the inaccuracy caused by preaveraging of hydrodynamic interactions (as estimated by computing exact and preaveraged first cumulant of the structure factor) does not seem to obscure the essential conclusions.