  Materials following Murray's law are of significant interest due to their
unique porous structure and optimal mass transfer ability. However, it is
challenging to construct such biomimetic hierarchical channels with perfectly
cylindrical pores in synthetic systems following the existing theory. Achieving
superior mass transport capacity revealed by Murray's law in nanostructured
materials has thus far remained out of reach. We propose a Universal Murray's
law applicable to a wide range of hierarchical structures, shapes and
generalised transfer processes. We experimentally demonstrate optimal flow of
various fluids in hierarchically planar and tubular graphene aerogel structures
to validate the proposed law. By adjusting the macroscopic pores in such
aerogel-based gas sensors, we also show a significantly improved sensor
response dynamic. Our work provides a solid framework for designing synthetic
Murray materials with arbitrarily shaped channels for superior mass transfer
capabilities, with future implications in catalysis, sensing and energy
applications.
