Mine rebloom through the summer, sporadically, Sometimes, they all fall over and I cut them back and get a whole new crop of flowers in a short time. If you cut off the seed pods, you will save yourself from becoming overrun. Once you have them, you have them forever, but they do fill up space nicely and I love their little three petal blooms. I have a clump down in front of the barn with hardy geraniums and hollyhocks for company - all on the northeast corner relatively out of harms way from marauding bovines and digging dogs.
In SE PA, they grow and multiply fine, but don't seem to self seed much if any. I've got a big white one in one bed that's been there for 10 years, and nary a seedling have I found. Only a few near some purples down near the creek. They do get a bit leggy in the mid season though.
The named variates seen to be pretty well mannered and fairly sturdy. We leave them alone.
The common purple can get a bit weedy looking and runs a bit.
Also tends to fall over in a heavy rain.
We cut the common one back to just above the first node before it sets seed and get a nice re-bloom.
I put in some "mixed" Transcendtia a couple of years about from one of those mail order companies and they are thicker than thieves. All of mine seem to be white (so much for "mixed"). They bloom well after rains and off & on through the summer. Guess I haven't noticed any seed heads on mine though. They are wonderful little flowers but each bloom is very brief. Mine are in heavy shade and fairly moist most of the time. Should I be doing anything differently to get more continual bloom?
Boy, did I butcher that botanical name!!! Should have read Tradescantia. I have cultivars Red Cloud, Red Grape and Navajo Princess. They have seed-headed, but not flopped yet. They're in full sun in a very wet area.
Dea- Maybe I'll try moving them to more sun. I have a direct sunlight area that's kind of boggy. Maybe I should try dividing some off my main planting to see if they'll do well there. Has anyone ever divided them?