Answer: Fortunately, thyme is easily propagated by cuttings. Simply cut a 3 or 4" long pieces of stem, remove all but the top inch of leaves, and "plant" them in a flat filled with moistened sterile seed-starting mix. Put the entire flat in a plastic bag, tie loosely, and set in a warm place. Check frequently to see that the soil doesn't dry out--try to keep it evenly moist. After about a month, gently tug on one of the stems, to see if roots have formed. A rooting powder may help speed up the root growth.
Another way to multiply the plant is to simply divide the plant and rootball into several smaller plants.
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