My neighbor calls it Queen Ann's Lace and it spreads by runners under the ground as well as drops seeds. If it's the same plant you'll have no problem with it coming back.

Ammi majus (bishop's weed, false bishop's weed, bullwort, greater ammi, lady's lace, Queen Anne's lace or laceflower) is not the Queen Anne's Lace I know (Daucus carota, also called wild carrot, bird's nest, bishop's lace). Ammi majus is an annual, IIRC, and does not have runners. Daucus carota is a biennial with a long taproot (culinary carrots are also D. carota, but they are the subsp. sativus). There's another plant, Aegopodium podagraria, which is also often mistaken for Queen Anne's Lace and is also called bishop's weed or goutweed, and that one is a perennial invasive weed with very aggressive runners/tubers. It took me about 2 years to get rid of the Aegopodium podagraria in my yard. I had to dig out a whole bunch of soil by hand and screen out all the roots and runners. I definitely don't want THAT plant back, LOL.

Common names as confusing as heck. That's why I prefer to call Ammi majus by its scientific binomial.

Yes, it does reseed sparingly...but is often late to emerge and very fragile. Worth saving the seeds and sowing in pots overwinter, mainly to protect the small seedlings from trampling (in my garden, an ever-present danger) or generally being overlooked.