I'm a photographer and I like taking pictures of interesting headstones, and headstones with interesting names or inscriptions.
I'm generally a polite, genial sort. If you ask me to transfer management of one of your relatives' memorials, I probably will -- just state your relationship, and be polite and patient. If it's one of my relatives, I probably won't, unless you're more closely related.
I believe that Find a Grave is a great collective resource for genealogists and gravers alike. As a general rule, I don't get hung up on who owns what, and I'll never be overly proprietary about memorials; if you want to add something pertinent to one of mine, please feel free. (One caveat: my photographs are all copyrighted to me. If I see them being used elsewhere, I will not be polite or genial about it. In advance, thanks for respecting that.)