Is there a small business law that allows use of copyrighted images if they are not m produced? (eg tattoo)?

Why can tattoo artists recreate copyrighted characters and logos? Is this due to the fact that it is a one-time piece of artwork, and not a m-produced product? I cannot find any conclusive information on the subject. I am interested in starting a business creating personalized products, and I need to know the finer details of small business copyright law to see if it would be possible.