This will depend upon the pro involved, but generally there are indeed pro fees. If the amateur just covers the pro's cost of attendance, then the pro wouldn't actually make any money off doing the comp (in fact, it's possible that they would lose money because of teaching time lost by traveling to a comp).
In my case, I normally pay for the following things: event entry fee, pro's admission for the session in which we compete, some portion of his travel/lodging (depends upon how many students are going), a per dance pro fee, and a per day pro fee.
The fees may also be different if the teacher competes with a pro partner. For instance, when my teacher and his wife were competing, they didn't ask me to pay travel/lodging costs when I "went along" with them to a comp. Basically (and thankfully!), they didn't charge for the expenses they would have incurred without me.