Gail, I have never heard of ageratums reseeding to that degree and they are annuals. What you have must have an extensive root system. When the plants get 4 leaves, pull them out. When they re-apear spray them with Round-Up.It comes in a variety of strengths, so get the strongest you can find. Then I would cover the area with wet cardboard, followed by 3 inches of organic mulch. If any new shoots appear paint the leaves with Round Up. Best And Happy Yardening, Nancy.