Multimolecular micelles are excellent delivery vehicles with one major flaw: they spontaneously disassemble and release their cargo when the concentration of unimer falls below critical micelle concentration. One way to circumvent critical-micelle-concentration-based instabilities is to tether the unimers together at the center of the micelle and generate a unimolecular micelle. Star-shaped block copolymers (SCPs) represent a possible material for unimolecular micelles - as long as the molecules can be engineered to avoid self-aggregation. Amphiphilic SCPs, with central hydrophobic blocks surrounded by terminal hydrophilic blocks, can be used for the solubilization of hydrophobic solutes. With the intention of rationally designing a stable unimolecular SCP, we use atomistic molecular dynamics simulations in explicit solvent to systematically evaluate the solution properties of hydrated SCPs successively as unimers, at high concentration, and in the presence of a small molecule drug mimetic. In these studies, the average number of water molecules bound per PEG repeat unit was comparable to experimental results. As well, the water accessible surface area of the PCL core was highly correlated with the molecular weights of PCL and PEG moieties. We postulate that the propensity for aggregation of SCPs is due to hydration of hydrophobic moieties in the unimeric state. SCPs with a PCL core less than 2kDa per arm are predicted to be fully protected from water and may form thermodynamically stable unimolecular micelles at low concentrations when the PEG blocks approach 14.6kDa per arm. Accordingly, simulations of SCPs at high concentration confirm that aggregation reduces exposed hydrophobic surfaces. Finally, simulations of SCPs in the presence of small molecule drug mimetics are performed in an attempt to predict drug loading properties and the impact of drug loading on SCP aggregation.