Systematic investigations of ternary In-based amorphous oxides, In–X–O with X = Sn, Zn, Ga, Cd, Ge, Sc, Y, or La, are performed using ab-initio molecular-dynamics liquid-quench simulations. The results reveal that the local M–O structure remains nearly intact upon crystalline to amorphous transition and exhibit weak dependence on the composition. In marked contrast, the structural characteristics of the metal–metal shell, namely, the M–M distances and M–O–M angles that determine how MO polyhedra are connected into a network, are affected by the presence of X. Complex interplay between several factors such as the cation ionic size, metal–oxygen bond strength, as well as the natural preference for edge, corner, or face-sharing between the MO polyhedra, leads to a correlated behavior in the long-range structure. These findings highlight the mechanisms of the amorphous structure formation as well as the specifics of the carrier transport in these oxides.