Ta Dove, I have several "tree peonies" which were bought as such. I have never heard of "tree poppies" though. And yes, you can grow "tree peonies" from cuttings. I did a couple, but they are very slow to establish and grow. my cuttings are 4 years old and still small. I do not know if I am doing something wrong or if it is just the nature of the plant. Maybe that is why they are not cheap to buy, although a couple of years ago one of the big online retailers were giving them away for just P&P in GW magazine. I received one as a pack of three. The other two were a magnolia and a hibiscus. They were sent as bare root plants and all are still alive.Younger form members with better memory might remember the offer, and you could enquire from the retailer.