Darlingtonia's produce many rhizomes or stolons from each plant, in fact it would appear much of the plants energy is devoted to this type of growth. In cultivation these rhizomes will often circle the plant pot several times before terminating in a new plant.
Roots are produced at various intervals along the rhizome, and it is not unusual to have several plants to each rhizome. This obviously provides an easy method of propagation. During the spring if a Darlingtonia is removed from its container it will usually be seen to have several rhizomes emerging from the main plant. Invariably there will be at least one fully formed plant at the end of one of the rhizomes complete with its own rooting system.
These can be removed with a sharp blade and potted up into the usual compost. Alternatively the rhizome can be divided into pieces, ensuring each section has its own rooting system. By burying the roots and ensuring each section remains on the surface of the compost, new growth should appear from each segment within 3 - 4 months.
It cannot be overemphasied that any disturbance to the rooting system should be done early in the spring months whilst the plant is still dormant. plants disturbed during the growing season may not recover until the following year during which time very little, if any, new growth is produced.