The flowers have 4 petals.

Galium species?

Hi pio. That is probably Juniper Leaf (Polypremum procumbens). It is really pretty, close up (photo follows).

{{gwi:282777}}

Thank you, Ruby. If there's a Galium like this, we're fortunate to not have it (if it's as annoying as the velcro-like one that does spring up in abundance in the spring.)

Heythere, Jekeesl, thank you. I think you've nailed it, and I think I asked about this same plant a couple years ago, name seems familiar but the one I tried to transplant at that time didn't make it, awful drought. It is pretty, I didn't want it to get mowed over the weekend although it seems to be a fine accessory in the lawn, not visibly different at a glance (except the cute little flowers) or unpleasant in any way.

Any species that is the only one of its' genus is a curiosity, IMHO.

FWIW, this native makes a much more interested potted plant than asparagus fern.