No sooner are you thrilled that a certain plant is thriving than it pops up unexpectedly where you didn't plant it. Then, before long, it has merrily spread its way through your garden.

Some reproduce themselves easily by seed, thanks to birds and breezes. Others spread aggressively by stolons (stems that creep along the soil surface, taking root and forming new plants at intervals). Eventually stoloniferous plants can choke out or smother their neighbors. Pulling or hoeing them barely fazes the plants; any stolons left in the soil just resprout. The upside to these lovely invaders is that they make good soil binders for slopes, and they grow where nothing else will.

The nursery plants listed below have aggressive tendencies that can make them nuisances for meticulous gardeners. Encourage the seed-spreaders where you want them, and pull up unwanted ones. You can restrain stolon-types by planting them in raised beds or in soil pockets surrounded by paving. Regularly dig out any unwanted shoots that do appear.

RUNAWAYS TO WATCH

Savvy gardeners develop strategies for using runaway beauties to advantage, letting them spread only where they want them. Some plants, however, cannot be safely controlled. In some regions, plants introduced as ornamentals have jumped the garden fence and threaten to crowd out native species or choke waterways. Scotch broom (Cytisus scoparius), with pretty yellow flowers, and purple loosestrife (Lythrum salicaria and related species) are examples. A good source for information on invasive plants is the website for the Federal Noxious Weed Program: www.aphis.usda.gov/ppq/weeds. Native plant societies in many states also maintain lists of problem plants.

SEED-SPREADERS

Forget-me-nots (Myosotis). True to their name, these demure little blue flowers refuse to be forgotten, persisting for years as they self-sow. Easy to pull where you don't want them.

Johnny-jump-up (Viola tricolor). This petite-flowered member of the viola clan is so loved, it's easy to overlook its habit of relentless reseeding. Easy to pull or hoe.

Jupiter's beard (Centranthus ruber). Self-sows prolifically thanks to small, dandelion-like parachutes on the seeds. Plant it in fringe areas; cut off old flowering stems to prevent self-seeding.

STOLON-SPREADERS

False dragonhead, obedient plant (Physostegia virginiana). Pink flower spikes resemble snapdragons; it's "obedient" only in that blossoms stay in place when twisted. To keep clumps within bounds, divide them every two years in spring.

Garden asters. Hardy, small-flowered types sold simply as garden hybrids quickly lace the soil with stolons and send up new shoots everywhere. Curb them in pots or raised beds.

Indian mock strawberry (Duchesnea indica). A trailing ground cover with wiry (and wily) stems that root; thrives among open shrubs or small trees. Flowers are yellow and single petaled; berries are small, nearly tasteless. Can be a rampant invader. If you must grow it, confine it to big pots with saucers, and display it on a paved patio.

Matilija poppy (Romneya coulteri). Six-foot-tall, gray green stems produce yellow-centered white flowers that resemble fried eggs. Plant in marginal areas such as on hillsides; keep away from less vigorous plants. Withhold summer irrigation to keep growth in check.

Mexican evening primrose (Oenothera speciosa). Pink, poppylike flowers bloom profusely in spring and summer. Will grow downhill, following water. Grow it in raised beds, or in planting pockets surrounded by paving.

Periwinkle (Vinca major). This blue-flowered ground cover has trailing stems that root wherever they touch the ground (useful on banks). But it's extremely invasive in sheltered, forested areas, and is on noxious weed lists in some states. Dwarf periwinkle (Vinca minor) is less invasive.

Russian sage (Perovskia). In mild climates, these woody perennials with blue spires spread rapidly even in arid soil, sending up whiplike shoots of silvery leaves that are difficult to pull.

Sweet violet (Viola odorata). Heart-shaped leaves and demure purple flowers belie this ground cover's boldness; it quickly carpets land where soil is moist and trees create semishade. Easy to pull.

Sweet woodruff (Galium odoratum). Low ground cover with pretty green leaves and fragrant white flowers. Spreads rapidly in moist, shaded gardens; can become a pest if allowed to grow unchecked.