Kalanchoe orgyalis. You might be tempted to feel the leaves but the fuzz rubs off. Edit: Aww... I was too slow ^

Agj, Because they're actually missing the very bottom of the plant, its base, where the stem & rosette attach. Ill advised to root it w/ no stem whatsoever, as it would likely rot the very base of the plant & cause the whole thing to collapse. I wouldn't remove any bottom leaves at all, for fear of the same thing. I've never seen 'cuttings' of rosette type succulents w/ NO BASE or STEM at all. It's not something folks would normally do, if they'd grown these themselves as they'd know better, or anything that'd be done by folks who actually know these plants, that's why I'm suggesting return them if PURCHASED. Cuttings even if unrooted are comprised of the entire plant. Different if from a well-intended friend if they didn't know better. I once brought back a shopping back literally stuffed w/ cuttings from friends of a friend in San Diego. All the rosettes had some stems left on them at least an inch if not more. It's sort of the minimum that one needs. Imagine one quarter of a king size bed covered w/ newspaper & all sorts of succulent cuttings; almost all made it. For at least some of us, it doesn't have to be hit & miss at all. Since this person sounds like a Newbie, imagine if they plant these in soil & then watered? Major mush would likely follow. Kate: they are beautiful. From the IDs given, if you do some reading, you'll see they mostly require similar care; strong sun (except the Haworthia), moderate watering, small clay pots (must have holes in them) & fast draining mix. Good luck.

Thank you! I've just picked them up, so I haven't had much time to accommodate them, as I know they are growing a little big for their pot! I only live in the UK, so not much sun here, I'm afraid, but I do have a UV setup. Thanks for all the help! Edit: How do you know that the soil is the wrong type? Are there any indicators I should look out for? Thanks again!

Sempervivums are very difficult to ID, there are more than 50 species and thousands cultivars, with many looking very similar. Exact name of the cultivar really doesn't matter that much as far as their needs: they are really same. When plant is not healthy, or grown under not-so-good conditions, they may, and often do, different than they should and that's another problem to ID it correctly. Kirby I don't see you mentioning your general location or growing zone? Sempervivums are very hardy plants, most of them will overwinter outdoors, under the snow, in z4 and many even lower. So unless you are in colder location, they could and should be grown outdoors. Proper pots are much more important than one may think. I would encourage you to repot plants that are in containers that do not have drainage holes. You don't even need to buy pots - plastic containers from cottage cheese or yogurt will work as long as you poke holes in it - a thin nail or straight pin works very well. Many small holes around bottom are great. Use opaque containers, as see-through will encourage growth of algae (more of a aesthetic problem, it will not kill your plants). I hope you do not think that we are preaching to you - all members here are quite enthusiastic about succulents; everyone that posted wanted to offer some helpful tips. We do get carried away - as soon as any of us see a problem, we comment even if you didn't ask about it (potting mix and drainage holes in this case...). It is all meant well and to help - otherwise none of us would waste time on reading and replaying :)