Branched or fractal-like extended surfaces are commonly found in natural systems and in engineered systems such as heterogeneous catalysts to enhance the rates of heat or mass transfer, or chemical reaction. Simple models can be derived to simulate the effectiveness and efficiency of these structures and provide some speculation concerning transport limitations affecting the evolutionary design of natural branching structures. Though the surface area of branching structures increases with each successive generation, their efficiency and effectiveness quickly approach asymptotic values. The transport limitations inherent in the structures render subsequent branching ineffective. Such limitations, characterized by environmentally driven, external transport resistances, may affect branching patterns found in plant root systems, mammalian motoneurons, and animal circulatory systems