Better understanding of the equity impacts of automated vehicles (AV) is needed to design equitable deployment plans for AV technology. The goal of this study was to develop and demonstrate a modeling framework to support distributional equity assessments of AV systems prior to their wide adoption. This modeling framework takes a disaggregated approach that integrates agent-based simulation, diverse transportation outcomes, and equity analyses. The framework uses individual-level data to capture detailed disparities in transportation outcomes, applies a state-of-the-art multi-agent traffic simulation model (MATSim) to simulate privately-owned and shared AVs simultaneously, and considers distributional equity from multiple perspectives. To test and demonstrate the framework, a case study was conducted for the Tampa Bay region. Five scenarios were considered with different AV market shares and integration strategies based on scenario planning by the U.S. Federal Highway Administration. Results reveal that high AV penetration rates were required for substantial reductions in inequality. The introduction of AVs led to a more even distribution of accessibility, but slightly more uneven distribution of traditional mobility and affordability. Impacts of disparities in outcomes for disadvantaged groups were mixed. These results suggest that AVs will likely perpetuate existing inequity in the transportation system as long as its fundamental structure remains the same as today. Results highlight the importance of planning and design strategies that directly address the distributional impacts to ensure that AV technology is deployed equitably.