The frequency co dependent storage G'(omega) and loss G"(omega) moduli of star-shaped polystyrene (SPS) molecules of a range of functionalities f and molecular weights per arm M-a were measured under small amplitude oscillatory shear conditions. Star-shaped macromolecules are composed of an inner region, core, where the chain segments are stretched and the "packing" density is higher than that of the outer region, corona. The frequency dependencies of G' (omega) and G"(tau) for low functionality molecules (f < 8) with long arms M-a are well described by the model of Milner and McLeish, indicating that the translational dynamics are facilitated by an arm retraction mechanism. With increasing values of f and decreasing M-a the model fails the arm retraction process is no longer valid due largely to the increasing size of the core in relation to the overall size of the molecule. The molecules exhibit evidence of spatial structural order due to entropic, intermolecular interactions, and the translational dynamics of these molecules occur via a cooperative process, akin to that of soft colloids, for sufficiently large values of f and small M-a. The overall dynamics may be summarized in a diagram delineating different mechanisms that facilitate flow as a function off and M-a.