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One promising approach to leverage existing complementary capabilities is allowing humans to delegate individual instances of decision tasks to AI. However, enabling humans to delegate instances effectively requires them to assess several factors. One key factor is the analysis of both their own capabilities and those of the AI in the context of the given task. In this work, we conduct a behavioral study to explore the effects of providing contextual information to support this delegation decision. Specifically, we investigate how contextual information about the AI and the task domain influence humans' delegation decisions to an AI and their impact on the human-AI team performance. Our findings reveal that access to contextual information significantly improves human-AI team performance in delegation settings. Finally, we show that the delegation behavior changes with the different types of contextual information. 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