>> some language on the tag that it is not allowed to be propagated, and I assume these must be copyrighted cultivars. I further assume this means one can't propagate for sale, but certainly one can divide or take cuttings from the plant for one's own use?
This came up on another website, and there was agreement that some forms of protection forbid ANY asexual propagation, even in your own garden for your own use, or for giving away for free. Thus it is technically illegal, but unenforceable. And very widely done. You might try sending an emAil to the breeder or patent holder, and asking to buy a few metal tags for a few dollars each, but they would probably tell you to go ahead as long as you keep the numbers reasonable.
I think that is "propagation prohibited" meaning "asexual propagation prohibited".
Is that the exact same thing as "patented"? I'm not sure.
You can always collect hybrid F2 seeds from a plant that is "asexual propagation prohibited" because seeds are sexual propagation. They just won't come true 100%. And you breed with pollen from that plant, or cross-pollinate that plant with something else. That's all sexual propagation, and doesn't produce the exact same plant.
Is there a kind of protection that forbids collecting or selling seeds? I think so, such as Monsanto has in force. But I can't find that old thread or my notes.
But the Plant Police don't often descend on private gardens and take DNA samples. In fact, I've read that usually the only enforcement mechanism is that the breeder can sue people if he can find evidence without trespassing.
I never understood who would sue who when a protected plant sends out runners and propagates itself.
P.S. Here is a list of different methods of asexual propagation. They all produce clones and they are all prohibited the same way:
Grafting and Budding