Researchers seeking alternatives to traditional desktop computers have begun exploring the potential collaborative benefits of digital tabletop displays. However, there are still many open issues related to the design of collaborative tabletop interfaces, such as whether these systems should automatically orient workspace items or enforce ownership of workspace content. Understanding the natural interaction practices that people use during tabletop collaboration with traditional media (e.g., pen and paper) can help to address these issues. Interfaces that are modeled on these practices will have the additional advantage of supporting the interaction skills people have developed over years of collaborating at traditional tables. To gain a deeper understanding of these interaction practices we conducted two observational studies of traditional tabletop collaboration in both casual and formal settings. Our results reveal that collaborators use three types of tabletop territories to help coordinate their interactions within the shared tabletop workspace: personal, group, and storage territories. Findings from a spatial analysis of collaborators' tabletop interactions reveal important properties of these tabletop territories. In order to provide a comprehensive picture of the role of tabletop territoriality in collaboration, we conclude with a synthesis of our findings and previous research findings and with several relevant design implications.