Constructal design has been applied to a large variety of problems in nature and engineering to optimize the architecture of animate and inanimate flow systems. This numerical work uses this method to seek for the best geometry of a T-Y assembly of fins, i.e., an assembly where there is a cavity between the two branches of the assembly of fins. The global thermal resistance of the assembly is minimized by geometric optimization subject to the following constraints: the total volume, the volume of fin-material, and the volume of the cavity. Parametric study was performed to show the behavior of the twice minimized global thermal resistance. The results show that smaller cavity volume and larger fins volume improve the performance of the assembly of fins. The twice minimized global thermal resistance of the assembly and its corresponding optimal configurations calculated for the studied parameters were correlated by power laws. (C) 2008 Elsevier Ltd. All rights reserved.