My lovely Podophyllum 'Spotty Dotty' is surrounded by babies. I kept referring to them as "seedlings" until I realized this plant spreads by rhizomes. It sends up erect growing stems from buds on the rhizome which produce a single, umbrella shaped leaf. You don't, however, get flowers until there are two leaves.
I had to laugh once I figured this out as it is so obvious from this photo. Look how all these new plants are growing in a row, shooting up along the length of the rhizome which I've indicated with that green line. At least that's how it looks to me. There is a similar line of spotted babies on the other side of the "mother" plant. In a few years this will be a spectacular clump if I'm lucky.