Crystal architectures delimited by sinuous boundaries and exhibiting complex hierarchical structures are a common product of natural biomineralization. However, related forms can also be generated in purely inorganic environments, as exemplified by the existence of so-called "silica-carbonate biomorphs". These peculiar objects form upon coprecipitation of barium carbonate with silica and self-assemble into aggregates of highly oriented, uniform nanocrystals, displaying intricate noncrystallographic morphologies such as flat sheets and helicoidal filaments. While the driving force steering ordered mineralization on the nanoscale has recently been identified, the factors governing the development of curved forms on global scales are still inadequately understood. In the present work, we have investigated the circumstances that lead to the expression of smooth curvature in these systems and propose a scenario that may explain the observed morphologies. Detailed studies of the growth behavior show that morphogenesis takes crucial advantage of reduced nucleation barriers at both extrinsic and intrinsic surfaces. That is, sheets grow in a quasi-two-dimensional fashion because they spread across interfaces such as walls or the solution surface. In turn, twisted forms emerge when there is no foreign surface to grow on, such that the evolving aggregates curve back on themselves in order to use their own as a substrate. These hypotheses are corroborated by experiments with micropatterned surfaces, which show that the morphological selection intimately depends on the topology of the offered substrate. Finally, we demonstrate that, with the aid of suitable template patterns, it is possible to directly mold the shape (and size) of silica biomorphs and thus gain polycrystalline materials with predefined morphologies and complex structures.