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Controling automactic mounting USB storage devices

All my machines have MATE desktop. They are various releases of Jessie and Stretch.

If the USB device is connected at boot, the individual partitions can be unmounted.

However, if the device is connected after boot individual partitions can not be unmounted with the GUI.

What controls this action?
An acceptable alternative that when connected the device is not automatically mounted but just appears in the Places menu.