There is a white flowered form of Mazus, but I don't suppose that's it otherwise you wouldn't be asking :-) Could it be Pratia angulata? Flowers aren't quite the same shape but otherwise bears a close resemblance.

Is it Blue Star....?

Here is a link that might be useful: groundcover

This may be an example of a name change.

I know it is NOT the same as Laurentia fluviatilis, which I also have, which was called blue star creeper when I got it and it is now called Pratia pedunculata.

Whether it is Pratia angulata, aka Lobelia angulata, I'm also not sure, that name is just not sounding right as what it was called when I got it. Maybe there was another common name for the latter and that is was I keep trying to remember.
Does P. angulata run above ground or just underground?

Pratia pedunculata creeps for me more by white underground stems, while this plant stays definitely above/ on the ground and sends down roots at nodes.

IÂll have to wait til it flowers again and get a better look at the flowerÂit is not a "star" shaped flower-- IÂm positive of that, though.

thanks