Tattoos and moral rights: a couple of points to ponder

Apologies are owed to my correspondent who wrote me the following missive, which I meant to post last week but completely overlooked. He writes:

"My colleague and I were discussing, at length, the art of tattooing (it was, after all, Friday afternoon!).

My question is this, if a tattoo artist creates a unique design for a client, then this is tattooed on to the aforementioned client, does the tattoo artist still own any intellectual property rights (namely copyright) over this piece of art? If the tattooed subject were to go on to a profession (I can only think of modelling at this precise moment) where the tattoo was constantly broadcast to the general public, and the designer viewed this to be derogatory to their work, would they be able to litigate!"

It seems to me that the potentially derogatory public display and transmission of the tattoo is only one of a number of moral rights issues that can be discussed -- another one is whether, if the tattooed subject wishes to have the tattoo amended or removed, the tattoo artist has any ground upon which to object.

Readers' thoughts on the topic are naturally welcomed.