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The effect of disorder on confined metallic cavities with an Aharonov-Bohmflux line is addressed. We find that, even deep in the diffusive regime, largevalues of persistent currents may arise for a wide variety of geometries. Wepresent numerical results supporting an anomalous scaling law of the averagetypical current $< I_{typ}>$ with the strength of disorder $w$, $< I_{typ}>\sim w^{- \gamma}$ with $\gamma < 2$. This is contrasted with previouslyreported results obtained for cylindrical samples where a scaling $< I_{typ}>\sim w^{-2}$ has been found. Possible links to, up to date, unexplainedexperimental data are finally discussed.Comment: 5 pages, 4 figure

Persistent currents in diffusive metallic cavities: Large values and anomalous scaling with disorder