Effective management of riparian areas in watersheds requires that reach-scale knowledge of riparian functioning be carefully 'scaled up' to provide models for entire stream networks. Weller et al. (1998: Ecological Applications 8, 1156-1169) describe a useful heuristic model for the network-scale average transmission of landscape runoff materials through a variable-width riparian buffer. Their model demonstrates that a variable-width buffer is likely to transmit more runoff materials on average, from adjacent landscapes into a stream than would a fixed-width buffer of the same mean width. By extending the Weller et al. (1998) model, I show that analogous results are true for arbitrary distributions of buffer widths and for other riparian functions such as woody debris input and stream shading. I apply the extended model to woody debris recruitment from natural tree-fall in variable-width riparian forest standards. The application suggests that the average number and volume of tree boles falling into a stream network will be overestimated, if the estimate is based on the average width of the network's riparian standards.