Polybutadiene star polymers, of nominal functionality 3, 4, 8 and 12, all with arm lengths of approximately 30 000 g mol(-1), have been synthesized using chlorosilane coupling agents. Dynamic mechanical studies have been carried out using parallel-plate rheometry at various temperatures, and the data frequency-temperature shifted to produce master curves. Fits to the Ball-McLeish constraint release theory indicate an effective entanglement molecular weight somewhat higher than the literature value for a linear polymer. This has been interpreted by considering a dilution of constraints effect caused by the Rouse diffusion of the terminal section of the star arm, leading to a predicted modified entanglement molecular weight similar to that found experimentally. Evidence for the Rouse-like behavior of the terminal section has been obtained from deuterium NMR spectra of a selectively deuterated sample. The presence of small amounts of residual linear chains is shown to be responsible for a further dilution of entanglements. An extension of the theoretical fits to include the high-frequency Rouse mode spectrum shows a divergence between theory and experiment which is indicative of the onset of the glass transition.