Suppose we have a parallel plate capacitor with two plates of unequal areas. Now we connect them across a battery and both will get equal and opposite charges. But, will the charge be distributed uniformly over the two plates or will it be present only in the overlapping area of the two plates?
Even when the plates are of the same size, the charge is not uniformly distributed over the plates: closer to the edges, charge density is lower than in the middle and there are some charges on the outer surfaces as well.
If the plates are not of the same size, the density near the edges of a larger plate will be much lower, but it still won't be zero and there still will be charges on the outer surfaces.