Children and even infants have clear intuitions about power early in development; they can infer who is dominant and subordinate from observing a single interaction. However, it is unclear what children infer about each individual's status from these interactions--do they think dominants and subordinates will maintain their status when interacting with novel partners? In three experiments, we investigate this question. Children (4- to 10-year-olds, N = 365) heard stories about a dominant and subordinate agent and predicted the dominant or subordinate agent's behavior with a novel agent. In all studies, we found that 7- to 10-year-olds generalized dominance, thinking the dominant would again be dominant or "in charge," both for social power (e.g., granting permission) in Study 1 and physical dominance (e.g., a fistfight) in Studies 2 and 3. Furthermore, although they believed dominant agents would win dominance contests (fistfights), they did not believe they would win contests unrelated to dominance (math contests). Younger children did not generalize social power (Study 1) but did generalize physical dominance (Studies 2 and 3). However, even for physical dominance, their generalizations were less selective (i.e., they believed the dominant would win fistfights and math contests). Notably, neither age group generalized an agent's submissiveness in any of the studies--they did not believe a subordinate agent would again be subordinate when paired with a novel partner. We discuss how these results extend past work on children's developing intuitions about dominance and prompt deeper questions about the inferences children draw from dominance interactions.