This paper is a proposal to embed tree-shaped vasculatures in a wall designed such that the wall withstands without excessive hot spots the intense heating that impinges on it. The vasculature is a quilt of square-shaped panels, each panel having a tree vasculature that connects the center with the perimeter. The coolant may flow in either direction, center-peri meter, or perimeter-center, although here only the center-perimeter flow direction is illustrated. Numerical simulations of conjugate heat and fluid flow in three directions show that it is possible to determine all the optimal geometric features of vasculatures with up to three levels of bifurcation (n = 3). The global performance is evaluated in terms of the overall thermal resistance, pressure difference, flow resistance and pumping power. The improvements in global performance diminish as the number of bifurcation levels increases. No flow architecture is universally superior. The dendritic designs are superior at the low and high ends of the pressure difference range. The radial designs are superior at intermediate pressure difference numbers. (C) 2009 Elsevier Ltd. All rights reserved.