It is possible that the majority of your procedure may be performed by someone other than your surgeon, especially if you are having your surgery at a teaching hospital.
At a teaching hospital, often a university affiliated facility, a resident may play a major role in your procedures. This is how surgeons and other types of doctors are trained: by performing their job under the watchful eye of an attending physician. In addition to surgical residents doing surgical training, anesthesiology residents and student nurse anesthetists may also play a role in your case.
The consent form you sign often indicates that a resident or someone other than your surgeon may participate in the surgery. If you don't read the document closely, or discuss the issue with your surgeon, you may find out after the fact that the majority of your procedure was performed by a resident.
To be clear, many residents have had several years of training in a variety of procedures, and are skilled practitioners in their own right. However, there is no guarantee of their level of training, and they could be in their first year of surgical education. Again, the work of residents is typically closely supervised by a fully trained physician, but they have not completed their own training.
If you are uncomfortable with having anyone other than the surgeon and a fully credentialed anesthesia provider participating in your surgery, you must discuss this with your surgeon. You should also take care to indicate your preferences on your consent form--if it allows for residents to participate in the procedure--so there is no question of who is performing your surgery.
Surgery Safer at Teaching Hospitals. Nicole Fawcett. The University Record, University of Michigan. Accessed April 2010. http://www.ur.umich.edu/0304/Mar08_04/13.shtml
You're Not Doing My Surgery, Are You? David A. Quillen, MD. Journal of The Association of American Medical Colleges. Accessed April 2010. http://journals.lww.com/academicmedicine/Fulltext/2003/03000/_You_re_Not_Doing_My_Surgery,_Are_You__.8.aspx