They will take pictures of the tattoo and plaster them on their myspace pages, they will start coming in for the tiniest tattoos and request a certain tattoo artist, they will bring in their friends to meet their cute "tattoo artist" and they will find reasons to hang out at the shop. Most tattoo artists recognize a groupie and don't have any respect for them, they are more of a pain to the tattoo artist than anything.
They try to get the tattoo artist to have sex with them. They get tattoo's in private areas. They try to make the tattoo artist's partner jealous. They act like they own the shop.