one for the legalisti

Hypotethically speaking, if one were to purchase something online and
then the vendor delivers two of the product when only one was requested
and paid for, does the vendor have any rights to ask for the extra

Of course - it's a mistake by them. At their expense though - you have no
obligation to post it. They can either collect or you can insist on them
sending you funds up front to cover postage etc

product back?

Is there a specific time limit after which the recipient may consider
the extra item to be theirs for keeps?

No. Well, I suppose until limitation has passed which is 6 years away.

Did it state on the delivery note/picking list that two were delivered?

Sorry, this is a hypothetical question so can't say. I'm not sure what
difference it would make anyway?

If it did, chances are, they'd never trace their missing unit to you.

If we find we're missing anything significant, or a customer claims
significant shortage, we go through recent orders and check things like
weights and dimensions. Occasionally we spot a double up, or half,
compared to expected , at which point we or