This paper is a proposal to vascularize a solid wall with transverse tree-shaped channels with fluid flow from side to side. The purpose of the fluid flow is to intercept in counterflow the solid heat conduction caused by an intense heat flux that lands on the exit plane of the wall. Tree architectures with 1-4 levels of bifurcation are simulated numerically, as a conjugate (convection and conduction) heat flow phenomenon in three dimensions. The effect of local pressure losses at junctions and entrances is included. The numerical work covers the Reynolds number range 10-550, svelteness number range 2.2-11.5, wall porosity range 0.01-0.1, and pressure drop number range 3 x 10(5)-10(10). The objective of the tree flow is to keep down the peaks of hot spot temperatures and the fraction of the volume occupied by high temperatures while using minimum pumping power. It is shown that the tree design is very effective, and that there is an optimal number of bifurcation levels for a specified porosity and pressure drop number. Tree designs are more effective than designs with parallel channels when the pressure drop number and the porosity are sufficiently large. (c) 2008 Elsevier Ltd. All rights reserved.