Cotton on small branch (4)

I believe the answer is:

twig

This clue is a double definition.

'cotton on' is the first definition.
(both can mean to realise something)

'small branch' is the second definition.
(I've seen this before)

(Other definitions for twig that I've seen before include "Suddenly see - bit of a tree" , "Suddenly realise" , "Understand; sprig" , "Small piece of tree" , "very little from box, perhaps" .)

I've seen this clue in The Telegraph, The Guardian and The Sun.

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