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Don’t worry, if you decide to change your mind and maintain ownership of the Mac, you can always reauthorize the computer again through the same menu.
Now that you’ve backed up everything and deauthorized the computer through iTunes, you will want to securely erase the entire hard drive so that none of your personal data could ever be recovered by the new owner(s). This is done by rebooting the Mac from Recovery Mode and targeting the primary partition with a secure format:
This may take a while depending on which security method you chose. 35-pass takes the longest because it is overwriting any data on the disk 35 times, if you choose that method expect to wait a while, particularly with larger hard drives.
Note for Macs with SSD / Flash Storage: Simply erasing the drive is sufficient for Mac users with SSD drives, and the security options are intentionally greyed out in Disk Utility (though there is a workaround if you’re committed to privacy). This is because data recovery is very difficult on an SSD to begin with, due to how flash storage works alongside TRIM to store, overwrite, and clear blocks on the drive.
When finished, exit out of Disk Utility to return to the OS X Utilities menu to proceed with the last step.
You’re almost done! The final step is to simply reinstall OS X so that the new owner receives the Mac as if it was brand new, complete with the initial setup screens and all. Unless you are using a boot installer USB drive, this process requires internet access so that the installer can be retrieved from Apple’s servers: