Dealing with branching passages, oil branch freely (9)

I believe the answer is:

bronchial

'dealing with branching passages' is the definition.

'oil branch freely' is the wordplay.
'freely' indicates anagramming the letters.
'oil'+'branch'='oilbranch'
'oilbranch' is an anagram of 'BRONCHIAL'.

(Other definitions for bronchial that I've seen before include "of lung passages" , "affecting tubes" .)

I've seen this clue in The Independent.

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