Solid-state additive manufacturing (AM) via friction stir based processes is gaining increased attention as these techniques are feasible for several similar and dissimilar material combinations and induce significantly lower energy input to the subjacent structure than fusion-based approaches as material melting is avoided. Available research concentrates on linear depositions; however, further development of these techniques towards application necessitates more complex deposition paths, e.g. curves and the crossing of edges of previously deposited layers. In this study, the solid-state layer deposition process of friction surfacing (FS) is investigated in terms of process behavior and appearance of the resulting deposit when curved deposition paths are applied. With advancing side on the curve's inner edge, material build-up occurs predominantly on this side of the layer, which results in a deposit of inhomogeneous thickness. This phenomenon is related to the FS process characteristic due to the superposition of rotational and travel movement on a curvature, and is more pronounced for curves with small radii. A further challenge exists for closed structures, where the deposition has to cross previously deposited layers. This can be successfully achieved by reducing the travel speed prior to passing the edge to provide sufficient plasticized material thickness below the stud tip. Overall, the study provides an understanding of the FS process behavior and process parameters for curved paths. Furthermore, recommendations for process control and path planning, e.g. for building closed cylindrical shell structures, are deduced.