My cat used to do this all the time. I always found that if you found some way to acknowledge the cat for its work (pat it on the head when you see what it left you) it would soon take the rest away and finish it off. I think it means the cat like you. After all, you likely feed it most of the time, its just trying to return the favor by leaving some if the food it caught for you.

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Jason Priest
1999 E430
1995 E420 - retired
1986 420SEL - retired