In this paper we develop an analytical and graphical formulation of the constructal law of maximization of flow access in systems with heat and fluid flow irreversibilities and freedom to change configuration. The flow system has global performance (e.g., minimization of global flow resistance) and global properties, or constraints (e.g., overall size, and total duct volume). The infinity of possible flow structures occupies a region of the two-dimensional domain of "global performance versus freedom to morph". This region of "nonequilibrium flow structures" is bounded by a line representing the best flow structures that are possible when the freedom to morph is limited. The best of all such structures are the "equilibrium flow structures": here the performance level is the highest, and it does not change even though the flow architecture can change with maximum freedom. The universality of this graphical and analytical presentation is illustrated with examples of flow structures from three classes: flow between two points, flow between a circle and its center, and flow between one point and an area. In sum, this paper presents an analytical and graphical formulation of the constructal principle of generation of flow architecture. The place of this new and self-standing principle in the greater framework of thermodynamics is outlined. (C) 2004 Elsevier Ltd. All rights reserved.