Dunites in the mantle section of the Oman ophiolite represent conduits for chemically isolated melt transport through the shallow mantle beneath oceanic spreading centers. These dunite melt conduits exhibit a scale-invariant power law relationship between width and cumulative abundance, as measured over 4 orders of magnitude. We use this size/frequency distribution to assess several hypotheses for dunite formation and estimate the total melt flux that a dunite network can accommodate beneath an oceanic spreading center. Dunites, measured from one-dimensional lithologic sections and digital image mosaics at a variety of length scales, range in width from ~3 mm to ~100 m and follow a power law with a slope of ~1.1. Extrapolation of the power law predicts that dunites as wide as 3.5 km may exist in the melting region beneath a mid-ocean ridge. Alternatively, perhaps the widest dunites we observe (~100 m) represent a maximum size. Modeling of dunites as diffusive reaction zones around melt-filled hydrofractures cannot explain the existence of dunites wider than ~10 m in Oman. Instead, dunites may represent high porosity conduits formed by reactive porous flow. Using the observed size/frequency relationship, the assumption that dunites form a coalescing network and the requirement that flux is conserved where dunites merge, we estimate the total flux through a porous dunite network and the fraction of that flux that remains chemically isolated. Our flux model predicts that the porosity in a dunite scales with the width. For maximum porosities of ~1--4% in the widest dunites, a network of porous dunite conduits with the abundances observed in Oman can supply a sufficient flux of melt (of which > 95% remains chemically unequilibrated with shallow residual peridotites) to satisfy the observed mid-ocean ridge flux.