What is the maximum size of an auger? For wood, auger bits don’t run much over 2 inches, since the torque would be difficult to handle. I am sure there are exceptions, but from experience, you really don’t want to have a larger bit on a portable drill, a drill press, of course, would be different.
For the real deal, I have operated a 36 inch earth auger installing foundations for signs and columns, but that was a little guy. Highway crews operate augers on heavy equipment that bore 6 foot holes, and there are some larger, but that is as big as I have seen. I don’t think you want to hook one to a conventional drill to spin them, either, but good luck!