Zero-field magnetization states in Permalloy thin film elements of rectangular shape are calculated by means of finite element micromagnetic modeling. The energies of several possible magnetization patterns are determined for different sizes and thicknesses of the specimen. Based on these data, a phase diagram of the lowest-energy configuration is set up for rectangles of edge lengths between 250 nm and 1000 nm. It is shown that a thickness- and size-dependent transition from quasi-homogeneous single-domain states to demagnetized flux-closure patterns occurs in that range. The regime of sizes and thickness of the phase diagram in which the lowest-energy configuration of the thin film element is a single-domain state is particularly important, since in this case the sample is expected to show good stability with respect to thermal demagnetization, which is a required criterion to make it suitable for technological applications in magneto-electronic devices.