The emergence of agentic Artificial Intelligence (AI), which can operate autonomously, demonstrate goal-directed behavior, and adaptively learn, indicates the onset of a massive change in today's computing infrastructure. This study investigates how agentic AI models' multiple characteristics may impact the architecture, governance, and operation under which computing environments function. Agentic AI has the potential to reduce reliance on extremely large (public) cloud environments due to resource efficiency, especially with processing and/or storage. The aforementioned characteristics provide us with an opportunity to canvas the likelihood of strategic migration in computing infrastructures away from massive public cloud services, towards more locally distributed architectures: edge computing and on-premises computing infrastructures. Many of these likely migrations will be spurred by factors like on-premises processing needs, diminished data consumption footprints, and cost savings. This study examines how a solution for implementing AI's autonomy could result in a re-architecture of the systems and model a departure from today's governance models to help us manage these increasingly autonomous agents, and an operational overhaul of processes over a very diverse computing systems landscape that bring together computing via cloud, edge, and on-premises computing solutions. To enable us to explore these intertwined decisions, it will be fundamentally important to understand how to best position agentic AI, and to navigate the future state of computing infrastructures.