Here we determine the tree-shaped structure that facilitates heat transfer between it and the solid body in which it is embedded. The vascular design evolves toward configurations that provide progressively greater heat transfer per unit volume. Two solid domain sizes are analyzed: a small cube where the tree structure grows to the second-level bifurcation, and a larger cube where the tree design grows to fourth-level branches. We show that when the solid domain and growing tree structure do not interfere with each other, symmetry is a beneficial feature that promotes heat transfer. When the tree structure interferes with the boundaries, asymmetry is the better design feature, and because of it the tree structure fills the available conducting medium. (C) 2012 Elsevier Ltd. All rights reserved.