The kinetics of preferential adsorption of a series of amphiphilic star block copolymers having cores made of polystyrene, PS, and coronas made of poly(2-vinylpyridine), PVP, have been studied using in situ phase modulated ellipsometry. The stars have, on average, either 26 or 40 PS-b-PVP diblock copolymer arms with PS/PVP molecular weight ratios (Sly) of 1/1, 5/1, or 9/1. Preferential adsorption from dilute toluene solutions onto silicon surfaces tethers these topologically complex star copolymers through their PVP blocks, yielding an interfacial structure resembling a dome. The adsorption kinetics are concentration dependent and show two distinct regimes: an initial rapid adsorption is followed by a slow approach toward equilibrium that is dominated by relaxations and rearrangements. For all PS/PVP ratios studied, star copolymers having 40 arms exhibit greater final adsorbed amounts compared to those having 26 arms. A kinetics model that considers diffusion of molecules at the solid/fluid interface as well as surface relaxation/reorganization events is used to characterize the adsorption process. In general, while both processes are necessary to describe the kinetics of preferential adsorption of these materials, surface rearrangements dominate for the two stars having the largest size and number of arms. It is also found that star block copolymers having symmetric arms (PS/PVP = 1/1) approach adsorption equilibrium in agreement with random sequential adsorption (RSA) model kinetics, attaining final adsorbed amounts that are close to those predicted for RSA processes. In contrast, the asymmetric stars having PS/PVP = 9/1 and 5/1 are able to rearrange on the surface, reaching final adsorbed amounts that are greater than those predicted for RSA processes, suggesting surface relaxation/reorganization and possible stretching due to confinement occurring at the solid/fluid interface. The results reported provide key insights as to how composition and connectivity of highly branched soft materials impact their self-assembly and interfacial structure.