You can scoop up the entire plant, with the chicks still attached to the mother plant/hen, and repot. If you leave them attached, the chicks will grow and the whole plant will develop into a large clump. Or, you can detach the chicks from the mother plant (just pluck them off) and nestle them down slightly in the soil, and in a little time they'll root. And in that case the chicks themselves would become new mother plants to, eventually, offshooting chicks just like you described. If you want to pluck them off and start additional plants that will produce their own chicks, don't worry about having the "tentacle"; it's unneeded, and I keep just the chick and nestle it in soil a far enough distance away that it'll have room to grow to maturity and shoot off chicks of its own.

If you lose roots while repotting, do not fret over it. It honestly does not matter; the plant should re-root. Sometimes a little chick just will not put down roots, but usually they'll be fine. These will root and be happy in well-draining soil, and it doesn't need to be moist while the plants are without roots. I'd just caution you that hens and chicks will "melt" in too hot of direct sun--I move them to a shaded or indirectly lit area when temps get to around 80 degrees or higher. I've had 'em melt before, and at that point they're shot.

These babies are a delight, but grow fast. I was initially excited and splitting off chicks all over the place, and I now have more Sempervivum (hens and chicks) than I honestly know what to do with. I'm now giving them away to happy neighbors.

i bought one of the furry ones in winter and stuck it in a corner and for some reason forgot about it and just found it a few days ago ... it grew huge ! and i mean HUGE it was in a 6 inch pot with the little babies growing ou the side ... so im guessing these things grow very easily and fast !