The structure and dynamics of structure formation have been studied in model triarm star block copolymers composed of two crystallizable blocks (poly(ethylene oxide) (PEO) and poly(epsilon-caprolactone) (PCL)) and one amorphous block (polystyrene(PS)). Crystallization starts from the homogeneous phase. For the structure investigation, X-ray scattering, optical microscopy, and atomic force microscopy have been employed, whereas for the kinetics, we have used differential scanning calorimetry, optical microscopy, and rheology. In the stars, there is a competition for crystallization between the two crystallizable blocks which have similar mobilities and melting temperatures but crystallize in different unit cells (monoclinic vs orthorhombic). When the crystallizable block length ratio is 3 or higher, only the longer block will crystallize. For comparable lengths both blocks can crystallize-however, not within the same molecule-but the crystallinity, long period, and crystalline lamellar thickness are reduced with respect to the pure PEO and PCL. The latent heats, obtained in the isothermal crystallization calorimetric experiments, are analyzed in terms of the Avrami theory. Although similar Avrami exponents were found for all stars (n = 2, reflecting a disklike growth from heterogeneous nuclei), the crystallization times were different depending on the nature of the crystallizable blocks. Optical microscopy revealed the formation of different superstructures (spherulites/axialites) depending on the type of crystallizable block (PEO/PCL). The growth rates of these superstructures were obtained and analyzed in terms of a kinetic nucleation theory, and the fold surface free energies were extracted. Notwithstanding the larger specific surface of bulk PCL as compared to that of PEG, the fold surface free energies in the stars were similar to that in PEG, indicating a pure PEO crystal and mixing of the amorphous blocks with the PCL crystal. This is supported from the results of the atomic force microscopy measurements on thin films, which have indicated the formation of perforated PCL crystals.