Please post another image, one that shows us what's growing nearby.

Actually nothing special nearby

However, I think it might be helpful to mention the strage black roots of the plant

And a final photo of the old trunk, which was cut off (note the twigs coming out of it)

are these bits of new growth emanating from that stump? That last picture makes me wonder if it's not really a weed, as we typically classify them, but the roots of an old tree making a last ditch effort to come up. Take a piece and run it to a local nursery to see what what they say.

The leaves are actually quite attractive. But there are two ways to knock it a manageable level. Pull like your trees depend on it, maybe even dig into the roots a bit, or chemical kill one at a time.

Round-up as a spot treatment should help a lot. The foaming spray cans do a pretty good job of keeping it from overspraying. It's pretty safe as long as it doesn't get on the leaves of the plants you want. It doesn't travel through the soil much either. So if you don't' want to pull, then spray those little suckers on a calm morning, and they should die off in a few days. Then get a pre-emergent to keep new ones from popping up.

Here is a link that might be useful: Weed Identification

The roots look like typical tree roots. A pre-emergent won't stop new sprouts coming up from a stump, which is what this looks like, at least in the last pic. A pre-emergent prevents seeds from sprouting.

Thanks for the tips and follow-ups.
I did not have a chance to test the pre-emergent for now, but round-up does seem to have some effect over new twigs.
I'm still waiting to see if this will be enough.

Why are those roots so black?
The tiny threads coming out of the main roots are completely black.
Is it normal for some trees?

This post was edited by sgsg on Fri, Sep 13, 13 at 13:08

I can't make out the black roots you speak of very well but it is possible that the original tree/shrub was killed by Honey Fungus, Armilleria, and the shoots are its attempts at regrowth. If the black roots look like boot laces compare them with some Google images of this fungus.

Here is a link that might be useful: