Bifurcated structures are so common in nature that their ubiquity has fascinated artists, mathematicians, scientists and engineers for centuries, and many theories have been proposed to account for the mechanisms that govern their formation and growth. From a thermodynamic/biological point of view, since the construction of a bifurcation requires some energy and material input, and in nature no resource is consumed unless it offers an evolutionary return, this must be justified by a compensating gain for the resulting evolved structure. Goal of this paper is to show that the introduction of a single physical “costing” paradigm leads to a better understanding of the phenomenology of both natural and engineered branched systems and, possibly, to an improved design of the latter. The cost indicator proposed here is the equivalent exergetic amount of the primary resources required by the construction and operation of the bifurcation. In the case of engineered machinery the “equivalent resources” must be augmented with the inclusion of the so-called externalities: how this inclusion is implemented is in fact not an essential problem, the point being rather the recognition that such a primary equivalent exergy cost, called the “exergy footprint” is a more proper quantifier than purely monetary or purely entropic “costs”. Such an exergy model provides a rigorous explanation to some of the questions not addressed by the most popular models, and in particular to the problem of how the prevailing boundary conditions influence the onset and the growth of a single bifurcation. The assumption that the driving force behind the emergence of each single instantiation of a dendritic structure is a thermodynamic cost/benefit ratio leads to a general formulation that extends both the Hess-Murray law and the Constructal Theory. The simple results reported below confirm that in nature there is no deterministic implication in this evolutionary process: simply, ceteris paribus, branched structures consume (=destroy) less exergy, and thus can better exploit the resources available in their immediate surroundings. Furthermore, both the splitting ratio and the branch aspect ratio depend on the applied boundary conditions, and there is no “universally optimal” shape, but rather a variety of “case-dependent optimal” shapes. Equally enlightening results are obtained for engineered structures, and the new insight ought to guide the design and manufacturing of devices in which flow bifu