We have performed extensive molecular dynamic simulations on a simple bead-spring model for copolymers with comblike architecture. Monomers located at the main chain and at the arms are respectively denoted as S ("slow") and F ("fast"). The model parameters are selected in order to induce segregation in domains rich in one component and poor in the other. In particular, we investigate the case in which the linear homopolymer of F-monomers exhibits much faster intrinsic dynamics than the S-counterpart. As a consequence, a strong dynamic asymmetry between both components is still present in the self-assembled copolymer system. We investigate static and dynamic properties as a function of arm length and temperature. The fast component exhibits decoupling of self- and collective dynamics as well as strongly stretched relaxation. Stretching is an intrinsic feature and is not necessarily related to gradients of mobility. The observed qualitative bends are fully consistent with recent neutron scattering experiments on poly(n-alkyl methacrylates), suggesting that they are generic in comb copolymers with strong dynamic asymmetry.