We report an extensive simulation study of the self-assembly of amphiphilic ABA triblock copolymers dissolved in solvents selective for the middle B-block. The effects of copolymer composition, copolymer concentration, and A-solvent interactions on the morphologies and morphological transitions of the aggregates arc examined systematically. The simulations reveal that a rich variety of aggregates, ranging from spherical and rodlike micelles and vesicles to toroidal and net-cage micelles, can be formed spontaneously from a randomly generated initial state. Phase diagrams are constructed and rich morphological transitions are predicted. Chain packing in different micelles is investigated. The Simulation results are compared with previous observations or predictions for related copolymer systems.