I did a google search on this plant and the best advice out there came from a Gardenweb post! LOL! Someone had asked if they could root cuttings. This is the response:
"Dichondra will root all along its stem. Lay the stems along the soil and detach from the plant when it roots."

Now I would just root them in a vase or jar of water. Cut 4-6" of the stem, take off about 2" of the lowest leaves, put it in water and wait for the roots to grow. I root coleus this way and it works great. Don't leave it in a sunny window though, could burn the roots. If you would do what the GW post said, make sure the ground is kept moist until rooted. Once rooted well, it doesn't need all that water. It sounds like that plant would make a good ground cover too if planted in the ground instead of a pot.
I see you said this plant has self sown in pots. It could be that the stems rooted and you got new plants. I've read also that it does self sow easily. Maybe the flowers are really small and short lived so you don't notice them. Just a thought.
Anyways, I hope you have good luck rooting them!

Kat

Thanks for your help Kat, I think I'll try to root it & shake some over the path that I want it to grow on next season. One or the other should work!
Ei