Witch structure of the cell controls what goes in and what comes out of the cell?

Cell membrane.

Explanation:

Well, in the animal cells the outermost layer is the cell membrane and that is what controls what comes in and gets "shipped" out. In the plant cell, the out most layer would be the cell wall, but that provides structure and under that there is a cell membrane that controls what goes in and out.

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following gollum to the back entrance