What exactly is the check return process? When an item is returned it is mailed back to the person who wrote the check or is it mailed back to the depositor? If it is rejected who is mailed back to also?

It really depends upon the bank of first deposits policy as well as their agreement with their customer. Some items may be charged back to the depositor and mailed to them. Some customers want all of their returned deposited items sent directly to a collection agency.
Sorry that I'm not much help but each customer and bank are typically different.

One thing is certain. If a check is "bounced," it will not be returned to the person who wrote it. It goes back to the bank of deposit, and from there, Swedish Chef is correct -- it will depend on the agreement with its depositor (and sometimes on whether the depositor has sufficient funds left to cover the bad check).