Am I safe to assume that the largest texture in the mipmap set will be the texture square that you supply? (assuming that your texture square is <= GL_MAXIMUM_TEXTURE_SIZE).
It seems sensible for the mipmap to go larger than the supplied texture square to save time on linear magnification. There may also be more restraints on the maximum mipmap.
The biggest texture is always the size you supplied. Having a bigger one doesn’t seem reasonable to me, for a similar result you’d have to perform linear filtering anyway, and you would waste tons of texture memory for reduntant data, more cache texture misses…
Also maximizing an image is very easy and fast. Mipmaps are used to reduce the work when the texture has to be minimized + it yields to a better image quality.