Hey immmac,
That's a great question! Migrating should only transfer the data that you want onto another Mac. Removing files from the old Mac shouldn't make any changes to the new Mac because of Migration Assistant. See this article for more info: Move your content to a new Mac
You may have your Apple ID or iCloud accounts logged in on both devices. Make sure that you sign out of your Apple ID or iCloud accounts from the old Mac by following these steps below:
1. Choose Apple menu > System Preferences.
2. Click Apple ID, then click Overview. If you use macOS High Sierra or earlier, click iCloud.
3. Click Sign Out.
4. If you want to a keep a copy of your iCloud data on your Mac before you sign out, make sure that you select the appropriate checkboxes. Then click Keep a Copy.
5. If you want to keep a copy of your Safari passwords on your Mac, click Keep on This Mac.
Here's the resource with those steps above and additional info: Sign out of iCloud on your iPhone, iPad, iPod touch, Apple TV, or Mac
Also, see the steps from this article on what to do before you give away your Mac: What to do before you sell, give away, or trade in your Mac
We hope these steps and articles were helpful! Let us know if you have any additional questions.
Cheers!
