New York City's Pre-K for All (PKA) is the nation's largest universal early childhood initiative, serving over 64,000 four-year-olds annually. Stemming from the program's choice architecture as well as the city's stark residential segregation, PKA programs are extremely segregated by child race/ethnicity. Our current study explores the complex forces that influence this segregation, including the interplay between family choices, seat availability, site-level enrollment priorities, and the PKA algorithm that weighs these and other considerations. We find that a majority of PKA segregation lies within local communities, and that areas with increased options and greater racial/ethnic diversity exhibit the most extreme segregation. We also conduct a simulation that leverages family PKA choices to maximize site-level racial/ethnic diversity and reduce between-site segregation.