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Clipping polygon to get proportion of attribute value-automate!

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Hello,

I am trying to clip watershed polygon shared by two or more counties in such way that I would like to get area of watershed that falls in each county with proportion of attribute value (water volume).

For example: watershed has water volume(V) and Area (A) and falls in 3 counties. By clipping I will get new shape area ( i.e, a part of watershed, let's called them A1,A2 and A3) for 3 counties. Now I can calculate proportion of V for each county manually. But I wonder if there is any advance tool in ArcMap to achieve this process without manual calculation. May be python scripting ?

Thanks in advance !

PS: I have dozens of watershed shared by few hundreds counties.

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