Dependency theories of causal reasoning, such as causal Bayes net accounts, postulate that the strengths of individual causal links are independent of the causal structure in which they are embedded; they are inferred from dependency information, such as statistical regularities. We propose a psychological account that postulates that reasoners’ concept of causality is richer. It predicts a systematic influence of causal structure knowledge on causal strength intuitions. Our view incorporates the notion held by dispositional theories that causes produce effects in virtue of an underlying causal capacity. Going beyond existing normative dispositional theories, however, we argue that reasoners’ concept of causality involves the idea that continuous causes spread their capacity across their different causal pathways, analogous to fluids running through pipe systems. Such a representation leads to the prediction of a structure-dependent dilution of causal strength: the more links are served by a cause, the weaker individual links are expected to be. A series of experiments corroborate the theory. For continuous causes with continuous effects, but not in causal structures with genuinely binary variables that can only be present or absent, reasoners tend to think that link strength decreases with the number of links served by a cause. The effect reflects a default notion reasoners have about causality, but it is moderated by assumptions about the amount of causal capacity causes are assumed to possess, and by mechanism knowledge about how a cause generates its effect(s). We discuss the theoretical and empirical implications of our findings.