It grows in grove-like groups and mature plants have a wooden trunk that can get quite thick and often creeps along the ground or stands up slanted. Trunks are rather brittle and tend to break or collapse during winter storms. Grows on its own in a mediterranean climate, seems to be quite drought tolerant. Blossoms (if I remember rightly) are small and yellowish. Sometimes there are two different kinds of leaves on a twig - see second photo below. Roots seem to spread out close to the surface and break easily when one tries to pull out young saplings. It is nearly indestructible and regrows even after being dug under completely during construction work.

I think someone asked about this plant some months ago; I hope somebody will remember the answer.

Moved to Plant ID Forum.

Oh, lets just re-invent the wheel... Some sort of Wattle?

After some more research I think it might be Acacia saligna. Any other suggestions?

A wattle is an Acacia. As we haven't gotten to see the flowers or get a good close-up of a leaf, I wouldn't hazard a guess as to species. You will have to judge that.

The photos you sent show a more prostate plant. Could this plant be a tree, given the chance?

Knowing your location would also help. Can you update your information to include a location?

It don't lok like it . But from your description. It sounds like Johnson grass.
So id treat it as so ! Sounds like same qualities ! thats (dis-) 😬 plow it under. Each section of plant and each section of root will grow anew ! 😡 ya gotta dig it out. And as soon as it starts comin back very small dig it out again.so on an so on. Dats only way to get rid of it permataly !
Sorry 😫 Ya might say "roundup" well....
That will take many yrs. If ever. Ive been battling nutgrass 20+yrs and purslane also. To no avail. But i heard from another nga member to use boilin water . There post is somwhere on garden.org
😎😎😎"The cool gardener"

@Philipwonel this is a tree/shrub branch, not grass.

I think he was just comparing it to the evil ways of Johnson Grass - possibly quite appropriately.

Ahhh

@Daisyl, I don't have any photos of the flowers - didn't photograph it in early spring. The older plants of this kind are definitely trees, some with a prostrate thick wooden trunk, some more or less upright and up to 3 meters tall. As far as the location is concerned, I'm traveling around the Mediterranean basin. Anyway, comparing it with photos of different acacias makes me quite sure that it is an Acacia saligna. I'll settle for that.