In the American Hosta Society Glossary of Terms compiled by C.H.Falstad,III and published in The Hosta Journal Vol. 29, No. 1, page 25, you will NOT find any reference to the term 'eye'. Oddly though, if you follow Steve's link to the AHS Hosta Dictionary it is referenced, go figure. In common Hosta parlance the term is applied rather loosely to dormant buds as well as shoots, mostly shoots, which clearly is incorrect. They are only 'eyes' when they are dormant buds, which means the shoot has not yet begun to come up from it. In other words, you would only see 'eyes' if you were to dig up a dormant Hosta in the winter. As soon as the dormant buds begin to swell and start sending up cataphylls it ceases to be an eye, it is becoming a shoot, it is no longer dormant. So, odds are when someone says Nursery X sent me a 3-eyed Hosta, following incorrect, but common, Hosta vernacular they are telling you they received a plant, probably bare-rooted for shipping purposes, with 3 shoots on it and depending on when it was shipped, the leaves may have begun to unfurl. Personally I try to refrain from using the term 'eyes' on Hosta crowns, I prefer to use 'dormant bud' and 'shoot'. To me, eyes are what you find on a potato....but that's just me being pedantic. And I have to keep reminding myself that some Hostas do NOT exhibit a stoloniferous growth habit but a rhizomatous one. Stolons go above ground, rhizomes below. Pieter

LOL I bought a package of 5 peonys from Costco last week also and asked what to do with them until I can get them in the ground... I was told to get them in pots so thats what I did last week. I used a mix of seed germination potting soil and just straight potting soil and placed the peonys in a south facing window and I now have strong growth in all 5 pots. I only plan to keep them in pots until May when our last frost is. If you can pot them in soil for the next month or so until your last frost date and keep them in a south facing window you will have a head start on growth and you can plant them in the ground in a short time. I think if you wait and keep them in the store bought packaging until your last frost there is a chance the eyes may die off - that happened to me when I bought a pack of lily of the valley pips from Costco last year - I kept the pips in the orginal packaging and when I went to plant them they were all dead. Hope that helps!

Most tree peonies are grafts. What you are seeing is the nurse root sending up foliage. They will remove food from your tree peony. If they have buds I would allow one or more to bloom to see what the flower looks like. Couple of questions to ask yourself. Is the herbaceous flower something you want to keep? Sometimes they are quite nice. Did you plant the tp deep enough that it has developed it's own roots? You have a couple of options. Cut or pull the herbaceous stems now but you need to dig down carefully to see if you have roots coming off of the upper stem. This fall you should dig the plant checking for the tp's own roots on the upper part of the stem. If the roots are there cut the nurse root from the tp. Keeping if you like, give to someone, compost. Replant tp a little deeper so it will develop stronger roots. If there are no roots from the tp you need replant deeply with much of the tree peony stem below ground. Do not remove nurse root because the only nutritian the plant is receiving is from the nurse root. The idea is to plant the grafted tree peony deep enough that the nurse root dies and the tp portion sends out its own roots.

"My guess is that if a division of an itoh peony is planted sideways in the ground, it will force the entire length of the woody stem to become tuberous, or at least produce roots/tubers from each underground eye." A woody stem may root, but the stem will not become tuberous (different cell structure). You will have greater success with root division and maybe grafting hardened stems (w/buds) onto herbaceous rootstock.