Egghead drops in, wolfing spread with fork (6,3)

I believe the answer is:

branch off

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'fork' is the definition.
Although both the answer and definition are verbs in their base form, I don't understand how one could define the other.

'egghead drops in wolfing spread' is the wordplay.
'egghead' becomes 'boffin'.
'drops' suggests deleting specific letters.
'wolfing' indicates putting letters inside (wolf can mean to eat or swallow).
'spread' becomes 'ranch' (synonyms).
'boffin' with 'in' taken out is 'boff'.
'boff' placed around 'ranch' is 'BRANCH OFF'.

'with' acts as a link.

Can you help me to learn more?

I've seen this clue in the Sydney Morning Herald.

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