Depending on size,they could be seedlings,or just eyes from the main plant that came up a long ways from the parent plant.

Either way it should be fine to dig them up and pot 'em up!

Early in the season they may be eyes that do not yet have roots attached to these new eyes. If you dig and do not get roots then that eye is gone but you really don't lose much because the energy going to that eye will go to the rest of the plant.

Try it for the fun of it or dig gently and spray water to move the soil from around where roots would be if there are roots.

most hosta do not grow from runners ...though some are rhizomatic [i cant think of the proper spelling/term] .... few [relatively speaking] grow from rhizomes.. underground stems ....

odds are they are seedlings ... and they are NOT just like the parent ....

it would help to know the mature plant you are referring too ....

ken

They are Polar Moon, and Guacomole that I can name off hand, and the smaller ones look exactly like the big plants.

i would love to see a picture...

neither of those would come true from seed.. nor do they grow on rhizomes .... so i dont understand how they can be coming up 5/6 inches from the crown .... hosta just dont work that way .... unless a piece of crown broke off when you were planting them????

i am stumped .... ken

rhizomatous
having long reaching, underground horizontal stems; loosely spreading habit.

If memory serves me right neither of the 2 you mentioned are rhizomatous. Pick a straight line from the shoot to the main plant and start pulling some soil up with in the first few inch's in between the 2. If you don't see the runner continuing to the main plant then you do have a seedling

and some hostas are referred to as stoloniforous. Not sure yours are that variety though. I have a Yellow Splash Rim that is.

Teresa,
For some weird reason the American Hosta Society (AHS) prefers rhizomatous..

http://www.hosta.org/About_Hosta/dictionary_of_hosta_terms.htm#[S]

Interesting......... but do they prefer the term or did the person compiling the info not want to type in the definition over again. Just kidding. I think of them as the same.

I'll be going out to pull up some of the worst stoloniforous plants on the fact of earth today. I can't think of the name at the moment....they have leaves like tulips and little white bell shaped flowers in rows. Talk about hardy - I've been trying to rid my garden of these for 6 years.

lily of the valley ....

ken