This work relies on constructal design to perform the geometric optimization of the Y-shaped assembly of fins. It is shown numerically that the global thermal resistance of the Y-shaped assembly of fins can be minimized by geometric optimization subject to total volume and fin material constraints. A triple optimization showed the emergence of an optimal architecture that minimizes the global thermal resistance: an optimal external shape for the assembly, an internal optimal ratio of plate-fin thicknesses and an optimal angle between the tributary branches and the horizontal. Parametric study was performed to show the behavior of the minimized global thermal resistance. The results also show that the optimized Y-shaped structure performs better than the optimized T-shaped one. (c) 2006 Elsevier Ltd. All rights reserved.