Motivated by recent experiments searching for Majorana zero modes in tripartite semiconductor nanowires with epitaxial superconductor and ferromagnetic-insulator layers, we explore the emergence of topological superconductivity in such devices for paradigmatic arrangements of the three constituents. Accounting for the competition between magnetism and superconductivity, we treat superconductivity self consistently and describe the electronic properties, including the superconducting and ferromagnetic proximity effects, within a direct wave-function approach. We conclude that the most viable mechanism for topological superconductivity relies on a superconductor-semiconductor-ferromagnet arrangement of the constituents, in which spin splitting and superconductivity are independently induced in the semiconductor by proximity and superconductivity is only weakly affected by the ferromagnetic insulator.
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