From what I've seen just now, in the U.S. you have no control over
donated tissue (except perhaps for needing your permission if a commercial product is developed from the research), and you may have signed away your rights to ownership in a procedure/surgery consent form. I believe most institutions will send slides or a tissue block to another upon request if they still have it--I think the 15 years your were told is the required minimum storage time in many states.
Our bodies, not our cells? (2016)
Do-we-own-our-bodily-tissues (2012)
Donors Retain No Rights to Donated Tissue (AMA
Journal of Ethics, 2009)
I saw 2014 article title about
a Canadian court decision that you do own removed tissue.
Anyone interested may want to check for more recent cases--things can change.
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And what better occasion is there for telling the classic story about
the very old mohel who, upon retirement, brings all the foreskins he kept from decades of circumcisions to the shtetl leatherworker and says "Make me something nice with these." He's told to come back in two week, which he does. "Here is your wallet" the craftsman says, "Isn't it lovely?" "Yes," says the mohel, "but I brought you jars and jars of skin and this small wallet is all you could make?" The letherworker replies "It's not an ordinary wallet. You rub it and it turns into a suitcase."
Djin
"I have Bright's disease and he has mine" --S.J. Perelman