The general mechanisms of structure and form generation are the keys to understanding the fundamental processes of morphogenesis in living and non-living systems. In our recent study (Denkov et al., Nature 528 (2015) 392) we showed that micrometer sized n-alkane drops, dispersed in aqueous surfactant solutions, can break symmetry upon cooling and "self-shape" into a series of geometric shapes with complex internal structure. This phenomenon is important in two contexts, as it provides: (a) new, highly efficient bottom-up approach for producing particles with complex shapes, and (b) remarkably simple system, from the viewpoint of its chemical composition, which exhibits the basic processes of structure and shape transformations, reminiscent of morphogenesis events in living organisms. In the current study, we show for the first time that drops of other chemical substances, such as long-chain alcohols, triglycerides, alkyl cyclohexanes, and linear alkenes, can also evolve spontaneously into similar non-spherical shapes. We demonstrate that the main factors which control the drop "self-shaping", are the surfactant type and chain length, cooling rate, and initial drop size. The studied surfactants are classified into four distinct groups, with respect to their effect on the "self-shaping" phenomenon. Coherent explanations of the main experimental trends are proposed. The obtained results open new prospects for fundamental and applied research in several fields, as they demonstrate that: (1) very simple chemical systems may show complex structure and shape shifts, similar to those observed in living organisms; (2) the molecular self-assembly in frustrated confinement may result in complex events, governed by the laws of elasto-capillarity and tensegrity; (3) the surfactant type and cooling rate could be used to obtain micro-particles with desired shapes and aspect ratios; and (4) the systems studied serve as a powerful toolbox to investigate systematically these phenomena.