Star polymer droplets can be used used as scaffolds for tissue regeneration. Experiments of these systems demonstrate a variety of hollow, non-hollow, and porous structures. We perform dissipative particle dynamics simulations (DPD) of 10 million particles using HOOMD-blue on Blue Waters XK7 GPU nodes. Our simulations map the phase diagram of droplet morphologies as a function of hydroxyl density and star polymer architecture (arm length and number) and offers predictive power to direct future experiments. This system demonstrates the possibility of functional droplets composed of complex networks, with a hierarchy of scales that can be tuned for specific applications.