A model of structural transformations of amorphous into quasi-amorphous BaTiO3 is suggested. The model is based on previously published data and on X-ray photoelectron spectroscopy data presented in the current report. Both amorphous and quasi-amorphous phases of BaTiO3 are made up of a network of slightly distorted TiO6 octahedra connected in three different ways: by apices (akin to perovskite), edges, and faces. Ba ions in these phases are located in the voids between the octahedra, which is a nonperovskite environment. These data also suggest that Ba ions compensate electrical-charge imbalance incurred by randomly connected octahedra and, thereby, stabilize the TiO6 network. Upon heating, the edge-to-edge and face-to-face connections between TiO6 octahedra are severed and then reconnected via apices. Severing the connections between TiO6 octahedra requires a volume increase, suppression of which keeps some of the edge-to-edge and face-to-face connections intact. Transformation of the amorphous thin films into the quasi-amorphous phase occurs during pulling through a steep temperature gradient. During this process, the volume increase is inhomogeneous and causes both highly anisotropic strain and a strain gradient. The strain gradient favors breaking those connections, which aligns the distorted TiO6 octahedra along the direction of the gradient. As a result, the structure becomes not only anisotropic and non-centrosymmetric, but also acquires macroscopic polarization. Other compounds may also form a quasi-amorphous phase, providing that they satisfy the set of conditions derived from the suggested model.