We have synthesized and characterized rod-coil.diblock, triblock, and starblock copolymers of controlled molecular weight by stable free radical polymerization, where the rod part consists of "mesogen jacketed liquid crystalline segments" (MJLCP). The MJLCP segment examined in our studies is poly{2,5-(4-butylbenzoyl)oxystyrene} (PBBOS) while the coil part is poly(styrene). SAXS studies of the block copolymers at room temperature predominantly show only a first-order maximum in their SAXS spectra. Above the T-g of the two blocks (similar to150 degreesC) no phase-separated morphology could be detected in temperature-dependent SAXS measurements of the block copolymers. Slow cooling regenerates the morphology, indicating very slow ordering kinetics. The effects of variation in molecular architecture and increasing topological constraint in going from homopolymer to star block copolymer on melt rheology (i.e., viscosity, relaxation times, and activation energies) are reported. In the master curves of all the block copolymers and homopolymers studied, nonterminal behavior was observed at low shear frequencies along with the absence of an entanglement plateau. In the PBBOS homopolymer an increase in molecular weight resulted in a decrease in the modulus of the nematic phase that was associated with a greater extent of shear orientation. On varying the molecular architecture from homopolymer to diblock to starblock copolymer, a decrease in the complex viscosity was observed that is attributable to the presence of polystyrene as the second block and the effect of topological constraints on molecular relaxation. The activation energies also follow the same trend as complex viscosity and relaxation times.