The limits I mentioned include both subsidized and unsubsidized federal loan programs. Any further amount you receive is either a private loan or PLUS. PLUS loans are made to the parent on behalf of the student, and actually were dischargeable by the parents' bankruptcy last I checked.

The graduate school limits are higher, but still exist. Med school students, for example, simply cannot fund their entire education through federal loans. The maximum period you can get through federal loans in any circumstance is around $140K, and medical school almost universally costs more than that.