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Here are my notes for upgrading OSX if you have a very tiny hardrive.
If it is a major update then:
Download Big Sur and write to external drive with
sudo /Applications/Install\ macOS\ Big\ Sur.app/Contents/Resources/createinstallmedia --volume /Volumes/MyVolume
Free up space with tips/ideas from this thread:
If you use docker and dont mind rebuilding your images run this:
docker system prune -a
Delete local timemachine backup snapshots: (Just reboot afterwards to actually see the freed up space):
sudo tmutil deletelocalsnapshots /
Then run Big Sur installer from installer PS: Remember to make a backup with time machine backup to external before upgrading just for in case