US News and World Report has data from 697 ranked colleges. Of these:
- 544 schools (78%) reported that no graduate students were the primary instructor of any course. These include all except two "National Liberal Arts Colleges."
- The 10 schools with the most graduate students as primary instructor were all large public research universities. These 10 schools reported that 18-26% of their TA appointments were as the "primary instructor."
Purdue University is listed as the school with the highest fraction of graduate students as instructors of record. Their policy allows the department to assign courses to graduate students; it makes no reference to upper division or lower division.
As another case study, the University of California reports that "as students progress through their academic careers and enroll in upper-division and graduate classes, they receive more consistent exposure to full-time permanent faculty and smaller classes." More specifically, the policy at Berkeley allows graduate students to teach lower-division classes, but they do so under the supervision of a faculty member, who remains instructor of record. However, Berkeley does allow graduate students to be the instructor of record for an upper-division course, though usually in exceptional circumstances only.
Summary: about 80% of universities do not allow graduate students to be the instructor at all. Of the other 20%, most are large public research universities. There is less data about the courses to which these graduate instructors are assigned, but Berkeley is an example of one school that will "formally" assigns graduate students to upper-division courses but not lower-division courses.