When you say its "popping up all over your border" do you mean that this one plant is spreading itself out or that there are lots of different ones? Are the leaves prickly?
How tall does it get? It looks more like a shrub than a herbaceous weed from the pictures.

When you trace the stem back to the ground is there just one or a whole group of them growing from the same place?

Have a look round and see if there is a tree or large shrub outside your garden with similar leaves.

Could it be an Ash sapling? They grow very fast. Have a look and see whether there are black buds.

it could be an ornamentle top part grafted onto the root stock of what you think is a weed and that's taking over and will totally .

I don't think its ash - ash normally has fewer leaves on the stem than this and also they are much narrower and with smoother margins. I suppose it couldn't be that dreadful suckering shrub with tiny pink flowers and white snowballs whose name I forget? That would explain it popping up everywhere. I would dig around the places where its appearing and see whether there are long roots connecting the various stems. Also look to see whether there are any white berries on any of it. Have looked all through my tree book and can't match it.

I agree, not quite right for Ash. Do you mean Symphoricarpos albus, Snowberry? That has oval leaves, sometimes lobed but not pinnate like these.

Jasminepadden, could you post some more photos? One of a whole leaf, flattened out on a sheet of paper, with measurements, would be useful, also one of any buds you can see.