Left on their own, Sempervivum rosettes grow into tidy, mounding clusters. They are also particularly easy to propagate by hand because they produce new offsets or "chicks" on stolons (horizontal stems).  Cut or gently pull a chick from the mother rosette. Place the new offsets on well draining soil in partial sun and water regularly until it can establish mature roots. The propagation of hardy succulents is best done outdoors in the spring or summer.
Unlike other types of succulents, Sempervivum will almost never root from leaf cuttings.