Same neighbor has this plant from next door seeding itself on her sidewalk
It's needle-y, but soft. And it's only about 6" tall - great groundcover.

It's a spurge of some sort. Might be:

Cypress Spurge (Euphorbia cyparissias)

If so, you should know that it's generally considered to be invasive in North America and is classified as a noxious weed in at least one state (Colorado).

Interesting.

I have had euphorbia myrsinites, Euphorbia dulcis 'Chameleon', and Euphorbia polychroma 'Bonfire', all of which came to me from other gardeners and DO seed around, but not in an uncontrollable way.

I'm really interested to see which one this one might be.

I might mention it is not only soft, it is almost feather soft.

This is not it: http://www.visoflora.com/photo...

I didn't see any "bracts" (not sure that's the right word - "collars" would be a layman's word for them) around the flowers. But to be sure, I'd have to walk up there and look again.

And note that those pics were taken today.
My 3 spurges bloom in spring.

crittergarden said:Interesting.

I have had euphorbia myrsinites, Euphorbia dulcis 'Chameleon', and Euphorbia polychroma 'Bonfire', all of which came to me from other gardeners and DO seed around, but not in an uncontrollable way.

I'm really interested to see which one this one might be.

It is what Kent said, unquestionably - Euphorbia cyparissias. It is none of the ones you mention.

The source of its (Euphorbia cyparissias, that is) invasiveness is thin, thready rhizomes that are very difficult to control, since they're fragile. It also seeds very successfully, with seeds being cast some distance from the parent plant (as in many other Euphorbia).

I guess there may be some little "collars" in my second pic. - hard to see though.

cyparissias would be blooming now?

It normally blooms in spring but plants can re-bloom, needless to say. Alternatively, it may be this year's seedings that bloomed recently. I think you'd be hard-pressed to find any Euphorbia species that lacks the little "collars". Why don't you show a close-up of the flowers? Perhaps they are actually the seeds, which would explain why the "collars" are lacking.

Everything about it fits in terms of appearance and your description, including how it's filled that bed.

OK.

I was concerned I was "trespassing" with my camera yesterday, although I don't think she would mind, really.

The FIRST picture was from the yard next door to her, and of a well established clump, with buds just opening. That's where her seedlings are coming from.

I'd have to go back (which I will) to check on the "collars".

I didn't have the camera with me Tuesday, but I looked close at the flowers they DID have little collars.