With the rise of agentic AI, delegation emerges as a key factor in business and IT management. Yet, our understanding of the human-AI delegation process in the context of managerial decision making, and of the factors influencing this process, is still in a nascent form. The purpose of this study is to advance our understanding of the human-AI delegation process and to delineate how task type and individual characteristics affect human-AI interaction, as well as how this interplay affects task-related outcomes. Understanding how humans interact with AI to perform problems and decision tasks that present different sources of complexity is essential to shed light on whether AI design needs adjustments to cover specific requirements, or whether humans need training and enhanced qualifications to reach high-quality outputs.