Answer: You can divide your arenaria by digging and separating the plant, taking roots along with portions of the top, and replanting each division.
Asteriscus is shrubby in nature and a bit more difficult to divide. If the roots produce new shoots, you can divide the plant, making sure that each new shoot has a root attached. Otherwise, propagate by seeds or by stem cuttings.
One of my most helpful resources for plant propagation answers is a book entitled "The Complete Book of Plant Propagation" by Graham Clarke & Alan Toogood, ISBN# 0-7063-7079-1. It deals with cuttings, division, layering, grafting and budding.
Hope the above helps you make a successful journey into the world of plant propagation!
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