For cooling electronics with high heat fluxes, a lattice wick system is disclosed that has a plurality of nano tube wicking walls configured to transport liquid through capillary action in a first direction, each set of the plurality of granular wicking walls forming respective vapor vents between them to transport vapor. A plurality of nano tube interconnect wicks embedded between respective pairs of the plurality of nano tube wicking walls transport liquid through capillary action in a second direction substantially perpendicular to the first direction. The nano tube interconnect wicks have substantially the same height as the nano tube wicking walls so that the plurality of nano tube wicking walls and the plurality of nano tube interconnect wicks enable transport of liquid through capillary action in two directions and the plurality of vapor vents transport vapor in a direction orthogonal to the first and second directions.