If I untick 'Enable iMessage' in prefs on my MacBook Air, will that stop messages going to it? I only want them on my iPhone.
If I do the 'Delete account' thing as advised in one video, I am worried iMessage might not work on my iPhone either.
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You can do either.
Disabling your Apple ID in iMessage will allow you to quickly re-enable it if you choose to use it on your Mac at a later time.
Deleting your iMessage/Apple ID account from iMessage preferences on your Mac will not affect iMessage on your iPhone. The only thing that it will affect is your ability to send and receive messages, either iMessages or Text Messages, from your Mac.
You can also just deselect your Apple ID from iMessage as well. You would have to go this way:
Messages > Preferences
Enable this Account or deselect everything in
You can be reached for messages at.
And Slidmac07 is right, deleting the account on your Mac won't affect iMessages on your iPhone. :)