I'd never seen any sign of this until, when lifting offsets in March, 2011, I found this structure on one of the cordatum which does look as if a new shoot is growing from the existing roots.
But, on closer examination of the other side of the shoot, new roots can be seen coming from the base of it. I think this is an offset either in the process of forming or one which has been trapped within the old root system.
It is NOT a fresh shoot from last-year's roots.
However, another plant, (shown on the right), had similar buds breaking from the old roots which, on closer examinanation, had no disernable root structure of their own, (the fine roots seen in the picture at the far-right are coming from existing roots).
As I don't know the actual stages of offset production, it may well be that these are offsets in the process of forming where the original plant has died back before they can form their own roots.
I shall examine these again later in the year as there are signs of new root production from last-year's roots on both plants.
UPDATE, 2012 Neither plant survived!
2013
When lifting C cordatum, (25o1), in early May to gather offsets, the root system shown below was found.
There were five such growths, only one of which could be removed as an offset with its own roots, (marked as 'offset' on the first picture.
The other four were an integral part of the parent plant, which still had fibrous root growing from the basal plate, so the whole assembly was potted up to see what happens.
UPDATE, 2014
When the stem was checked in April of this year, all the original roots had rotted off but there were two young plants growing by the stem. A watch will be kept to see if any more of the four appear but it does seem that the growths observed in 2013 were offsets in the process of maturation. They are not part of the original plant.
2016
A cordatum offset flowered in its pot in September
