We went on the Imagination in Jan. 2003 and my daughter took a friend with her : age 13. We did this a couple of years ago and took 2 extra friends for my sons and they were 17 years old. The parents of the children wrote a letter like this:
(parents name) give permission for our daughter, (childs name), to travel out of the country with (our names) on the following dates: Jan 1, 2003 through Jan 7, 2003 (they put in 2 extra days just in case). In the event she needs medical treatment we give (our names) the permission to them to seek treatment in her behalf.
Both parents signed this letter and had it notarized.
Carnival never asked to see this letter but I had it in case they did. I had heard before we went on the cruise that carnival would ask for the letter but they never did and I wanted to make sure I had her birth certificate and letter to make sure there was no problem. When we ordered our plane tickets since her last name was different from ours hers(the friend) had to get a paper ticket and my family had electronic tickets. That was the only thing we had to do different by taking a friend.