I planted a small plant of oregano from a garden show last year. It easily quadrupled itself before winter came, and now that it’s spring, it’s raring to go again. I am going to have to divide it for sure. Is it invasive? One of my friends suggested that it was, so no one wanted any when I offered it.
I also bought 4 French tarragon plants, which are hard to find. Usually it’s Mexican (good enough) or Russian (don’t bother) tarragon. I left them outside instead of putting them in a pot and bringing indoors for the winter. Though the plants died back, all four have sprung forth, and three are looking really nice already. The fourth plant gets a little too much shade, I think, but it is just growing a bit slower.
Considering the way the stuff grows, I wouldn't be surprised at all that it's invasive. I've just started ripping the stuff up and tossing it.