The trade-off between exploration and exploitation is common to a wide variety of problems involving search in space and mind. The prevalence of this trade-off and its neurological underpinnings led us to propose domain-general cognitive search processes (Hills, Todd, & Goldstone, 2008). Here, we propose further that these are consistent with the idea of a central executive search process that combines goal-handling across subgoal hierarchies. The present study investigates three aspects of this proposal. First, the existence of a unitary central executive search process should allow priming from one search task to another, and at multiple hierarchical levels. We confirm this by showing cross-domain priming from a spatial search task to two different cognitive levels within a lexical search task. Second, given the neural basis of the proposed generalized cognitive search process and the evidence that the central executive is primarily engaged during complex tasks, we hypothesize that priming should require ‘search’ in the sense of a self-regulated making and testing of sequential predictions about the world. This was confirmed by showing that when participants were allowed to collect spatial resources without searching for them, no priming occurred. Finally, we provide a mechanism for the underlying search process and investigate three alternative hypotheses for subgoal hierarchies using the Central Executive as a Search Process model (CESP). CESP envisions the central executive as having both emergent and unitary processes, with one of its roles being a generalized cognitive search process that navigates goal hierarchies by mediating persistence on and switching between subgoals.