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How to Stop Receiving Messages on Mac
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On your Mac, open the Messages app.
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Click Messages in the top bar and select Preferences.
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The Accounts window will pop up, tap your Apple ID on the left column.
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Uncheck Enable this account.
That’s all it takes to stop getting messages on Mac. When you attempt to open the Messages app on Mac in the future, you’ll have to login. Doing so will allow messages to be received by your Mac once again. But you can always use this tip to make it stop.