How do I stop imessages from downloading on my macbook air after upgrading to ios8?

Hello catfish65,

After reviewing your post, it sounds like you do not want messages to go the the computer. I would recommend that you read this article, it may be able to help the issue.

iOS and OS X: Link your phone number and Apple ID for use with FaceTime and iMessage - Apple Support

On OS X, find out which addresses are enabled:

In Messages, choose Messages > Preferences > Accounts.
Select iMessage in the left column. Your contact preferences should appear under "You can be reached for messages at:."

Thanks for using Apple Support Communities.

Have a nice day,

Mario

Messages/Preferences/Accounts - select the Messages account and select Sign out.