Multi-person tabletop applications that require a high display resolution, such as collaborative web-browsing, are currently very difficult to create. Tabletop systems that support mixed-presence collaboration, where some collaborators are remote, are also hard to build. As a consequence, investigation of some important tabletop applications has been rather limited. In this paper, we present T3, a software toolkit that addresses these challenges. T3 allows researchers to rapidly create high-resolution multi-person tabletop applications for co-located or remote collaborators. It uses multiple projectors to create a single seamless high-resolution tabletop display, and allows multiple tabletops to be connected together to support mixed-presence collaboration. This engineering is hidden behind a simple, flexible API. T3 also supports existing user interface components, including buttons and spreadsheets, allowing the rapid creation of complex tabletop applications.