Balloon flowers can be divided in order to propagate the plant — just keep in mind that this is often extremely difficult, since they tend to only have a single, deep primary taproot. To divide the plant, begin by digging up the root system. Separate the clump into a few individual pieces. Make sure that each division can support itself with several healthy sections of roots. Plant each section and water immediately. Keep the area moist, applying a layer of mulch if necessary, until you see new growth. This will indicate that the roots have taken off and your propagation was successful.