Blood shear stresses (τwall) on the endothelium of the microvasculature have been shown to provide a stimulus for affecting endothelial metabolism and function, with ramifications which affect many physiological processes. Prevailing levels of τwall which generally equals the product of viscosity (η) and shear rate (γ), result from a complex interaction between network topography and the rheological properties of blood. To delineate those factors which affect this relationship, the distribution of blood flows (Q), γ, and microvascular hematocrits (Hmicro) were examined in parent and daughter branches of arteriolar and venular bifurcations in the intestinal mesentery by intravital microscopy. The results indicate that daughter to parent ratios of Q and γ, fall and rise, respectively, as daughter branch diameter (D) decreases relative to the parent vessel D. In contrast. Hmicro, the main determinant of η, remains relatively constant, suggesting that variations in η have a lesser influence on τwall at branch points. Analysis of flow apportionment at branch points in light of Murray's Law of optimum design,(Q-D1) suggests that network geometry alone does not adhere to this relationship, but that the resultant flow state gives rise to conditions which lessen variations of γ at branch points throughout the network.