We demonstrate that the competition of dendritic crystals in a solidifying sample gives rise to two qualitatively different micro-structure solutions depending on the density q of crystals in the melt. Here we show for the first time, that there is a non-steady transition from one to the other. The precise q-dependence of the transition point is determined by the Biot number. Our investigation is based on a scaling analysis for the tip velocity of the dendritic crystals, which we assume to be aligned in an array and to be coupled via the transport of heat. We develop our analytical solutions based upon the asymptotic Kruskal-Segur reduction to a differential equation in the complex plane. It is supported by numerical simulations of a multiscale model of alloy growth. On the one hand this solution can be used to improve the accuracy of applied solidification simulations. On the other hand it yields additional insight in the universality of diffusion limited crystal growth in the presence of competing micro-structures.1 The impact of micro-structure selection in computational materials scienceSimulating the solidification of a stable phase at the expense of a metastable phase is one of the elaborate multiscale problems of computational materials science. Starting from atomistic considerations of atom attachment over dendritic growth dynamics of a single crystal to grain growth and finally to the influence of material properties of macroscopic cast metals the phenomenon of solidification spans 9 orders of magnitude in length scale. For an understanding of the multiscale nature of solidification pathes models of dendritic growth at the scale of micrometers have played a central role. These models include the atomic dynamics via transport and attachment coefficients. Moreover, they allow for a coupling to macroscopic transport dynamics as will be discussed in detail in this chapter. Even the growth dynamics of a single dendrite is an intriguing and difficult problem posing analytical as well as numerical challenges. Since the late eighties great progress has been made on the question of what determines the structure of dendritic crystals [1]. Analytical advance was tied to the discovery of the impact of the anisotropy of surface tension on the selection of an isolated dendrite [2]. Morphology transitions due to anisotropy effects have been the subject of numerous studies since, see e.g. [3,4]. On the other hand, numerical advance was strongly tied to the development of phasefield models as numerical tools to overcome the numerical difficulties of the so called free boundary

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