Native moss

What does anyone know about that moss that tends to grow in planters and anywhere it is dark and wet? It's soft and gets pretty thick, sometimes 1-2 inches, gets teeny little flowers, pulls out easily in clumps, doesn't seem to have much of a root system. Maybe it's a fungus rather than a moss? I go back and forth about pulling it out or just letting it be. I think this may be the same moss that folks wage war with in lawns.

I have had a lot of different mosses. I generally take as much as possible off when I weed in the spring and then add either compost or garden soil to surpress it for awhile. I like moss, it is free green stuff, native and I like the old look it gives to pots and rocks and such.

I have read that moss likes acid soil so if you add a bit of lime it slows the growth. If there is rodies and such maybe not a good thing to add lime.

I'm not necessarily opposed to the moss, and if it is not in the way I just let it be. I can't for the life of me grow rhodies with any success, and have given up trying. And, as Willow notes, I do like it on my stumps and boulders.