Crossword Genius

Detective’s funds said to spread widely (8)

Ross

I believe the answer is:

disperse

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'to spread widely' is the definition.
(I've seen this before)

'detective's funds' is the wordplay.
'detective's' becomes 'di's' (Detective Inspector abbreviation).
'funds' becomes 'perse' (I can't explain this - if you can you should give a lot more credence to this answer).
'dis'+'perse'='DISPERSE'

'said' is the link.
I am not very happy about this link. It may belong to another bit of the clue.

Can you help me to learn more?

(Other definitions for disperse that I've seen before include "Thin out and disappear" , "Cause to separate and go in different directions" , "Scatter, dissipate" , "Spread widely" , "Scatter in all directions" .)

I've seen this clue in The Times.
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