Our garden in Christchurch New Zealand has been invaded this summer by what I have in my profound ignorance named stalky things. These weeds have a single, strong central stalk. No hint of flowers has been observed. Their roots are shallow: the largest specimen I have removed, shown below, has no more than 10cm of root supporting more than 1m of growth.
I'd be grateful for any hints toward identification. I'm happy to provide more information - I've never asked such a question before, so I may well have left out something obvious and critical.
Here is an uprooted 1.2m specimen:
And here are two smaller examples in the garden, the larger 30cm:
Added 14 February 2020:
After waiting until late in our summer for flowering of the plant, this has begun at the very tip of the largest specimens (>1m). Here is the detail: