Extremely desultory men falling apart (12)

I believe the answer is:

tremendously

'extremely' is the definition.
(tremendously can mean extremely or considerably)

'desultory men falling apart' is the wordplay.
'falling apart' indicates an anagram.
'desultory'+'men'='desultorymen'
'desultorymen' with letters rearranged gives 'TREMENDOUSLY'.

(Another definition for tremendously that I've seen is " Very much".)

I've seen this clue in The Times.

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