Do you recognise this weed?

[Flummery]

I'd leave a few to grow and see what happens. Aquilegia has a VERY deep root! My first thought was, like the others, Aquilegia, but I have a Thalictrum aquilegifolia (meadow rue) which, as the name suggests, looks VERY like Aquilegia until it flowers, lovely fluffy purple heads. Mind you, my Thal. has never seeded (would love it to) so if you're over-run it's sure to be Aquil.

[TPeers]

I have aquilegia in my garden and let it seed every year. It isn't a real problem plant and if you pull the plants up at this time of the year that will be the end of your problem. If you want some real problem plant I can offer bindweed, couch grass of mares tail, I have an abundance of all three.
Ian

So generous of you! Are you sure you can spare the plants?

I have Ground Elder to add to the list of hated plants!

I managed to buy a house and garden with NO aquilegias at all - amazing! I bought two last year, both bi-colours, so I am now waiting to see what I get.

As has already been said they do tend to have deep tap roots and are very free seeding. My plants were supposed to be F1's which I thought ment sterile - but presumably just means 'won't breed true' so it will be very interesting to see what colours I get.

Terry