A systematic study of the equilibrium chain exchange kinetics of a tunable model system for starlike polymeric micelles is presented. The micelles are formed by well-defined highly asymmetrical poly( ethylene-propylene)-poly( ethylene oxide) (PEP-PEO) diblock copolymers. Mixtures of N,N-dimethylformamide (DMF) and water are used as selective solvents for PEO. With respect to PEP this solvent mixture allows the interfacial tension, gamma, to be tuned over a wide range. The equilibrium chain exchange between these micelles has been investigated using a novel time-resolved small-angle neutron scattering (TR-SANS) technique. The results show that the exchange kinetics is effectively frozen for large interfacial tensions but can be readily tuned to accessible time scales ( minutes to hours) by lowering gamma. Independent of temperature and concentration, the corresponding relaxation functions show an extremely broad and heterogeneous logarithmical decay over several decades in time. We explicitly show that such broad relaxation cannot be explained by polydispersity or a classical distribution of activation energies. Instead, the logarithmic time dependence points toward a complex relaxation picture where the chains are slowed down due to mutual topological and geometrical interactions. We propose that the behavior stems from constrained core dynamics and correlations between the expulsion probability of a chain and its conformation.