Amorphous TiO2 (a-TiO2) could offer an attractive alternative to conventional crystalline TiO2 phases for photocatalytic applications. However, the atomic structure of a-TiO2 remains poorly understood with respect to that of its crystalline counterparts. Here, we conduct some classical molecular dynamics simulations of a-TiO2 based on a selection of empirical potentials. We show that, on account of its ability to dynamically assign the charge of each atom based on its local environment, the second-moment tight-binding charge equilibration potential yields an unprecedented agreement with available experimental data. Based on these simulations, we investigate the degree of order and disorder in a-TiO2. Overall, the results suggest that a-TiO2 features a large flexibility in its local topology, which may explain the high sensitivity of its structure to the synthesis method being used.