In this work we report the crystal growth of SmOFe_1−xCo_xAs single crystals with Co content 0≤x≤0.25 via the solid-state single crystal growth method at ambient pressure. The centrepiece of this method is to trigger the abnormal grain growth process, where only a small amount of grains grows significantly larger than the majority of grains. In its extreme case, this diffusion-controlled process in the solid state may foster large and three-dimensional crystals that grow out of a polycrystalline matrix. Since most parameters known to trigger solid-state single crystal growth are known only empirically, we discuss in detail which are the optimal parameters for the growth of SmOFe_1−xCo_xAs single crystals and rationalize the mechanisms that may be relevant to activate the diffusion-driven solid-state single crystal growth in the system under study. The plate-like crystals show distinct facets, which is a common feature of crystals grown by this method, with lateral dimensions of up to 4.8mm and a thickness of up to 0.06mm. The single crystals of this series as well as the corresponding polycrystals were characterized and compared regarding their crystal structure, chemical composition, morphology as well as magnetic and superconducting properties. Interestingly, our characterization data suggest a solubility gap for high Co contents. This finding is supported by comparing with previous reports, albeit existence of a solubility gap is not discussed therein. As expected across the series, charge doping suppresses the structural and magnetic transitions until for 5% Co content superconductivity is established. In particular, the splitting and clear differentiation of the structural and subsequent magnetic transition is rarely seen for REOFeAs compounds, but well resolved for the Fe-rich SmOFe_1−xCo_xAs single crystals and even for the x=0.0125 crystal, but smeared out for the corresponding polycrystalline samples. Hence, the SmOFe_1−xCo_xAs single crystal presented in this work are of exceptional high quality.