Alumina is historically a difficult material to characterize as a result of both its amorphous nature and the large range of densities and local atomic coordination topologies present. Alumina is ubiquitously employed as a high-dielectric-constant material in electronic devices, thus understanding the microscopic physics governing its structural and heat-transport properties is of key relevance for e.g. the design of heat management in these devices. Here we rely on first-principles techniques to characterize the structural, vibrational, and thermal properties of amorphous alumina across a wide range of densities, ranging from the record-low value of 2.28 g/cm 3 to the record-high value of 3.49 g/cm 3 . We show that the large variety of atomic coordination topologies coexisting in this material are responsible for the emergence of significant structural disorder at the sub-nanometer length scale. We apply the recently developed Wigner formulation of thermal transport in solids to characterize how the interplay between such strong topological disorder and anharmonicity affects heat transport, showing that topological disorder dominates over anharmonicity in determining the thermal conductivity of amorphous alumina.