Increasingly, more school districts across the US are using centralized admissions for charter, magnet, and neighborhood schools in a common enrollment system. We first show that, across all school-participation patterns, full participation in the common (or unified) enrollment system leads to the most preferred outcome for students. Second, we show that, in general, participation by all schools may not be achievable because schools have incentives to stay out. This may explain why some districts have not managed to attain full participation. We also consider some specific settings where full participation can be achieved and propose two schemes that can be used by policymakers to achieve full participation in general settings.