Single-chain Monte Carlo simulations of amphiphilic diblock dendritic copolymers (co-dendrimers) with single and binary trifunctional cores were carried out in continuous space using implicit solvent. Two distinct topologies were studied: dendrimers with the hydrophobic blocks attached to the core, and dendrimers with the polar blocks attached to the core. Both topologies were found to be capable of forming micellar-type structures. As well as in terms of simulation snapshots, the systems were quantitatively compared via asphericity characteristics, monomer density profiles, mean-squared distances of monomers from the center of mass, and mean-squared bond lengths. Increasing the number of generations or increasing the number of spacers between branch points both yielded more well-defined shapes. Although increasing the number of generations of branching initially resulted in more spherical conformations (as for homodendrimers), it was found that high generation co-dendrimers adopted elongated cigar-like conformations for the single core case and dumbbell-like conformations for the binary core case. This phenomenon appears to involve the dendron segregation which occurs at the core of these large co-dendrimers.