It may be easier if my questions are more specific:

Are above ground runners the only way Ajuga spreads? How far can a runner travel before it lands/roots in dirt?

Is a garden edger sufficient to contain Dianthus grianopolitanus and Lamb's Ear (Silver Carpet)?

Suggestions to keep them from running over each other?

Thanks!

Kay

You keep them in place by trimming and removing as needed--generally 2 or 3 times a year. It's basic gardening maintenance.

Ajuga will not fare well in a hot, dry, sunny situation. Also prefers an acidic soil condition. The other two should work reasonably well together, as neither spreads very aggressively...in fact they are seldom considered "groundcovers" but rather just low growing, moderately spreading perennials. As noted by lacey, just remove unwanted portions if they spread further than you prefer - no need for any edging.

I think I knew the Ajuga wouldn't do well there (it's been struggling to come back in my holding garden), but I've been in denial. Sad; it would be a nice contrast to the silver-green of the other two! Maybe Elfin Thyme to break it up? Had really wanted to do big root geraniums but there just isn't money for it.

The street strip is in front of an assisted living facility. I removed the grass last fall and have been prepping the ground for ground cover. We've since decided to sell. I doubt the new owners will want to do much maintenance at all. If I don't get some ground cover in I'm afraid they'll put in rock "mulch." My old people deserve better than that!

Since I won't be there to maintain, will garden edging keep the Lamb's Ear away from the tree trunks? As a novice, I let it grow up to a Rose of Sharon, on a standard, and it rotted the trunk.

Thank you for your help!

Kay

I have a Vinca Minor that is totally self sufficient, for 15 or 20 years. It is dence and about a foot high, and has only had one unwanted plant pop up, a birch tree. But I doubt it plays well with others.

I cannot think of ground covers that are low maintenance that would respect boundaries as you are hoping for. I have a small path to a faucet where I have three types of sedum ground covers that each are in their own area. They would spread into each others space, but I rip it up asap. It is so easy. I spend maybe 10 minutes on this a few times in the growing season.

I had a long path of mini Ajuga that went about 30 feet, It is verigated with pink and has purple flowers, I found it low maintenance, I loved it.