I'd remove them; IME 99.9% of the volunteers I find are not desirable. IDK what your plant is, check around the local area to see if you can find a parent plant or two.

Is there a Brazilian pepper nearby? I'm never very good at identifying plants from pictures, but if that's a BP, you probably want to grub it out. Unless you want a big tree there soon....

Ok, thanks to both of you. Not sure about the BP in the area. These are both so vigorous and healthy that I'm very suspicious of them! Probably will remove and let the star jasmine take over the little fence.

In Southern California, rarely ever will you get a desirable volunteer. I've gotten all sorts of things that started sprouting out of the bushes: Mexican fan palm, carrotwood, asparagus fern, and something that looks like American holly.

I did get an interesting one: something that looks like a fig has come up. Guess I'll have to wait and see whether it's a male or female.

That first pic looks like ailanthus. Really undesirable. Hard to kill. Nip it in the bud and get rid of it.

For me fig trees are frequent weeds, growing so close to desirable plants they almost impossible to remove the roots.

They were too tough to dig out. I clipped them off low, stomped remaining stems. They'll be back.

i often see volunteer figs.