Many perennials grow large "clumps" of roots from which numerous "instances" of the plant grow. When these clumps get too large, the plant becomes crowded (in the case of, for example, cone flowers or day lilies) or maybe just too big for the space (hostas, ferns, etc.).
Other perennials lose their vigor after three or four years. Some, like monarda (bee-balm) "donut," where the center dies out and the healthy part of the plant is on the outside of a ring. With these, you can dig up the whole plant, and cut the healthy parts into several individual plants. Then you replant one of the divisions and use the others in different places, or give them away to less fortunate souls.
As a general rule, the root clumps of perennials can be split into smaller sections and re-planted or shared. Thus, where one large plant existed, now three or four exist.
The process varies slightly from plant to plant, but basically, the large plant is dug up as intact as possible and, with a sharp knife, the root clump is cut. When you look at the roots, it should become obvious where to make the cut. The goal is to have significant root structure on each "division." (Although with some plants like day lilies, the amount of plant that is significant is pretty small....)
It sometimes helps to prune away foliage before this process is started. As with a large hosta, all that foliage is essentially in the way and makes the handling of the plant more cumbersome.
The best time to divide is often debated among gardeners.
Fall division and spring division each have merits. Spring time allows
the gardener to divide and see immediate results. The old foliage
is not in the way and the new shoots coming up depict a pretty clear "things
to come" for the season. Fall division seems to be a natural process
as the old foliage is being cleaned up and the garden is being prepared
for next year. When dividing in the fall, it is important to do so
well before the ground freezes in order for the roots to have a chance
to settle in to their new home.
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