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-I hope you don't mind me sending you one flower.
-I hope you don't mind my sending you one flower.

Could someone refresh my mind and tell me if both options are possible? Thanks in advance.
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A classic, Maj.

The logic is that in the first case, 'me', the person him/herself is a possible irritant, while in the second case, 'my', it is the sending of the flower that may be irritating. Therefore, formal grammar would require 'my'.

Practically, however, both occur, the former probably with more frequency than the latter in speech and informal writing, and with little or no confusion of meaning except for the pedant.
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See also the post "Me doing and My doing".