Since 1995, publicly funded pre-K with universal eligibility has proliferated across the U.S. Universal pre-K (UPK) operates at great scale and serves children with a wide range of alternative childcare options. Because these programs are relatively young, very little is known about their long-run impacts on children. In this paper, I use a difference-in-differences (DiD) design to estimate the long-run impacts of Georgia UPK, the first statewide program. Children exposed to UPK were 1.7% more likely to graduate high school, 11.1% less likely to receive SNAP benefits as adults, and girls were 10.6% less likely to have children as teenagers. To help interpret those results, I develop a simple conceptual framework that considers how public pre-K expansions can affect the entire childcare market. For instance, greater competition could force private centers to adjust prices and quality, or to close entirely--creating spillover impacts on children not enrolled in public pre-K. Empirically, I find evidence consistent with large spillovers in Georgia, suggesting that a focus on UPK enrollees would miss a key part of the program's overall impact. Further, I show that conventional DiD estimates of treatment effects on the treated may be substantially biased in the presence of spillovers--in the Georgia context and in others.