I assume it's a weed, since it grows so well. All replies are appreciated.
I think you're right - "carpetweed". Thanks rugbyhukr!
I didn't know Mollugo so I looked it up. I have to say I see little resemblance. Can you show the whole plant? If I had to give an opinion I'd say Iberis sempervirens from what I can see.
Here is a link that might be useful: Iberis sempervirens
Yeah, Mullugo has whorled leaves, more like Gallium. The plant in the picture has alternating leaves.