There are two commonly grown varieties... one that is larger and more bushy, and one that is more of a compact groundcover. And it sounds like you guys each got one of them.

Cuttings are the easiest way. I have the groundcover type. It roots where branches touch the ground. So all you'd have to do is dig up a portion, separate it from the rest of the plant, and then put it wherever you want. Keep trying. You'll get it.

Propagation

'Flora Sun' beach sunflower should be propagated by cuttings. Take 4-inch stem cuttings any time of the year, and remove all but the two terminal leaves. Cuttings should readily root without any rooting compounds* in 2 to 3 weeks under intermittent mist in a shaded (30% light exclusion) greenhouse. During warmer times of the year, we use a misting frequency of 9 sec/2.5 min, with cooling fans (fan/pad system) set to run at 90°F. A propagation heating mat may be necessary during cooler times of the year to maintain rooting medium temperature at 70°F.
Seed propagation is not recommended because 'Flora Sun' beach sunflower could hybridize with other sunflowers, resulting in seed-propagated plants with characteristics unlike those of 'Flora Sun'.

from this web site :

Here is a link that might be useful: Propagation and Container Production of 'Flora Sun' Beach Sunflower

interesting... i had never realized that there were two kinds, just figured that the lower, lusher ones got more water and fertilizer.

i have the larger, bushier version. every season, i throw out no fewer than 200 seedlings... they pop up everywhere. hundred feet from where they're planted.

my experience has been (granted, with the bushy version) that they transplant best when small. they also start readily from cuttings.

short answer, regine--next season, you'll have plenty of seedlings from both. the problem will be telling one from the other. and, maybe they'll hybridize??

Gotta love a plant that will take over a playground. I did a job for a private school here in Boca Raton many years ago. They wanted to have Helianthus planted at the base of the swings, the merry-go-round, the edges of the sandbox. Not a problem, I put in a few here and there by the fence line as well. Two years later and they called me to come back as the plant had completely covered the playground, was working its way into the parking lot, and several moms and dads had taken cuttings and were also complaining about this now out of control plant.

Best advice I can offer is to be careful where you plant it, it has a mind of its own.

Thank you all for your advice. It seems that the smaller one will be easier to control as it still has not needed pruning, but I'm getting ready to prune the big one for the third time! It's planted in the swale with a sidewalk on one side and the street on the other so I'm hoping it won't be too much trouble to keep it under control.

Regina

I just bought 4 of these from a local native nursery- and now I'm wondering which type I have. Mine doesn't seem bushy really, just seems to branch out, almost like a vine. I was wondering- if these do decide to send out seeds, how easy are the babies to pull from where they are not wanted?

I planted my yard with dune sunflowers and gaillardia to avoid having to have a lawn. At first both did well, spreading nicely and covering the ground with bright blossoms and healthy foliage. But now, five years later, the gaillardia are gone completely, and the dune sunflowers are barely hanging on in a few clumps here and there. What happened? Do these plants go through a natural cycle? How do they survive in the wild? I have an irrigation system operating year round. Should they not be watered? Help!

I have the ground cover variety (Helianthus debilis). It gets about knee high, but grows outward at an alarming rate. I love it because it flowers almost year round. It is one of the few things that is blooming in my yard right now.

I have found that it will propagate very nicely(badly) if you just trim it and drop the trimmings in a pile somewhere. (I have this pack rat/compost/lazy mentality that any clipping is good compost.) The good thing is it easy to pull out if it starts growing somewhere you don't want it to.