When are professors most free during a semester? You would think that profs are living the high life when lectures are over and all they have to do is to hand out the exam (in a couple weeks) and grade them. But when I tried to get a hold of the profs, they seem to be busier than ever. One prof even stopped holding office hours all together and handed those duties to the TAs.

What do profs usually do after all lectures has stopped, and in general, when are profs most free in terms of their faculty duties during a semester?
The end of the semester particularly the period between the end of lectures and when students finally leave campus (which may be well after you've submitted grades) can be the busiest part of the semester because that's when you spend a lot of time dealing individually with students that have questions, complaints, or problems.  The reason that this is so time consuming is that there are typically lots of these students, and each complaining student can easily take an hour out of your day.    

Meanwhile you may also be grading a lot of term papers or student projects and you're also busy writing, proctoring, and grading final exams.