Before revision:  We develop the theory by considering diffusive search in two distinct geometric configurations. First, we determine the mean and Fano factor of the distribution of resources between pair of concentric spherical targets, and explore how these depend on the initial location of the searcher, the dimension d, the degradation rate and the distribution of delays. Second, we use asymptotic analysis to determine the mean number of resources in each of N small interior targets within a three-dimensional bounded domain. In particular, we show that the mean number of resources in a target is proportional to its effective `` shape capacitance.
After revision:  We use this to show that the mean number of resources in a target is proportional to its effective `` shape capacitance.