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Modern client processors typically use one of three commonly-used power delivery network (PDN): 1) motherboard voltage regulators (MBVR), 2) integrated voltage regulators (IVR), and 3) low dropout voltage regulators (LDO). We observe that the energy-efficiency of each of these PDNs varies with the processor power (e.g., thermal design power (TDP) and dynamic power-state) and workload characteristics. This leads to energy inefficiency and performance loss, as modern client processors operate across a wide spectrum of power consumption and execute a wide variety of workloads. We propose FlexWatts, a hybrid adaptive PDN for modern client processors whose goal is to provide high energy-efficiency across the processor's wide range of power consumption and workloads by dynamically allocating PDNs to processor domains. FlexWatts is based on three key ideas. First, it combines IVRs and LDOs in a novel way to share multiple on-chip and off-chip resources. This hybrid PDN is allocated for processor domains with a wide power consumption range and it dynamically switches between two modes: IVR-Mode and LDO-Mode, depending on the power consumption. Second, for all other processor domains, FlexWatts statically allocates off-chip VRs. Third, FlexWatts introduces a prediction algorithm that switches the hybrid PDN to the mode that is the most beneficial. To evaluate the tradeoffs of PDNs, we develop and open-source PDNspot, the first validated architectural PDN model that enables quantitative analysis of PDN metrics. Using PDNspot, we evaluate FlexWatts on a wide variety of SPEC CPU2006, 3DMark06, and battery life workloads against IVR, the state-of-the-art PDN in modern client processors. For a 4W TDP processor, FlexWatts improves the average performance of the SPEC CPU2006 and 3DMark06 workloads by 22% and 25%, respectively. FlexWatts has comparable cost and area overhead to IVR.