This article explores how common misunderstandings about the microcirculation - that capillary supply varies directly with O(2) demand, that local capillary supply in muscle is determined by fibre type and that it is appropriate to model capillary distribution as either random or in a fixed geometric pattern - arise from quantifying capillarity by simple measures of quantitative extent, rather than the more functionally relevant qualitative distribution. We show that the latter approach reveals exquisite control of angiogenesis that determines the location of new vessels with astonishing accuracy, motivating a reappraisal of the physiological remodelling process and a new approach to computational investigations into peripheral O(2) transport.