There are many ways of doing this. What you need to know comes under 'licensing' of art.
It is up to you to decide what you allow and what you don't. Each part of your art can be specified.
There are books on Amazon and other places re 'licensing' artwork, and 'the business of art' as well as 'legal art forms'.
You can handle it yourself.
I used to do line drawings that were produced as rubberstamps. I didn't sell my original art or my copyright. I allowed my line art to be used for the producation of RUBBER STAMPS only, for a period of 2 years (or you can say - for 500 stamps only, e.g.). The rubber stamp manufacturer permitted hand-stamping only - thus not allowing the image to be produced professionally in any way.
I would have been free to also license the SAME image as a design on a mug, produced by another company with a similar agreement - and to any other offers. I was still able to produce e.g. mouse pads with the image, or cards, and to sell the original artwork and/or prints if I wanted to.
When you license things you can do it as a lump payment. e.g. $50 for the rubber stamp people. Or, you can get e.g. 3 cents for each kitchen souvenir oven mit that sells - usually you get a check every 3 months for something like that (royalties) ... and although that might not sound great, it can work out to a LOT of money over a period of time - more than you would have gotten for the lump sum.
Hope that is what you're asking, and hope it helps.
~Jillian
~Jillian
artist, Jillian Crider
... google me!