"migrating" to Mac Mini

How to move your content to a new Mac
https://support.apple.com/en-us/HT204350

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Connect the computers to each other
■ If both computers are using macOS Sierra or later, just make sure that they're near each other and have Wi-Fi turned on...if either is using OS X El Capitan or earlier, connect them to the same network using Wi-Fi or Ethernet
■ Or connect them using target disk mode and the appropriate cable or adapter. Then start up your old computer in target disk mode
■ Or connect your new Mac to a Time Machine backup of your old Mac
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How to use target disk mode to move files to another computer
https://support.apple.com/en-us/HT201462

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As an alternative to target disk mode, you can use AirDrop to send content between two Mac computers wirelessly.

 

Fishrrman's "you can do it!" routine for migrating to a new Mac:

If you follow my instructions below, I guarantee a success rate of 98%:
PRINT OUT these instructions and check them off as you go along.

1. BEFORE you do anything else, run a "final" backup on your old Mac. It can be either TM or a cloned backup using CarbonCopyCloner or SuperDuper. I recommend CCC.
2. Shut down the old Mac and disconnect the USB drive
3. Take the new Mini out of the box and set it up on the table. DO NOT PRESS THE POWER ON BUTTON until step 8 (read on). You don't want to begin setup until "the right moment".
4. Connect the display using the usb-c/VGA adapter/cable that you have
5. Connect the keyboard and mouse. I STRONGLY SUGGEST that you connect them DIRECTLY to the Mini.
6. If you use a hub, leave the hub DISCONNECTED for now
7. Connect your backup drive -- use the usb-c adapter if needed.

OK, we're ready-to-go, so let's get goin':
8. Press the power on button for the first time.
9. The Mini may ask for help "finding" the keyboard, just follow instructions.
10. Begin setup. At the appropriate moment, setup assistant will ask if you wish to migrate from another Mac or drive. YES, you want to do this.
11. "Aim" setup assistant at the external TM backup. Setup assistant will need a little time to "digest it all" (be patient)
12. You will now see a list of things that can be migrated, such as applications, accounts, settings and data.
13. I suggest that you select ALL of them.
14. Let setup assistant "do its thing". It's going to TAKE A WHILE to move things over. Again, be patient.
15. When done, you should see the login screen. Go ahead and login.
16. Once logged in, things should look pretty much as they looked on your old Mac.
17. You should check all your apps. Some may not run, and may require upgrading.
18. You could disconnect the old TM backup and set it aside, or ... "repurpose it" to become the backup for the new Mini. I'd keep the old one around for a week or so, at least.

 

Might be nice to know how much space you need on the mini. (?)
Are there multiple hard drives in your old MacPro? How much storage space is used?
How much is available on the mini?

 

Carbon Copy Cloner never disappointed me. It always perfectly cloned drives even in hot mode (while I was using the system).

 

For the migration, SuperDuper will work just fine.
Again, see reply #5 above.