Let's consider that we have downloaded network boot mini.iso (real Ubuntu version does not matter, but LTS is better).
How should I install minimal but functional MATE Desktop Environment from it?
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You have two options here:
Install minimal system and then install all needed packages with
sudo tasksel install ubuntu-mate-core
The resulting system will be small (about 4 Gb), but functional.
You can then adjust this basement to suite your needs.
ubuntu-mate-desktop^- see my other answer.
taskselto remove packages from the system (see this post for details)!