How to copy "just files" recursively

Use find:

find folder0 -type f -exec cp {} targetfolder \;

With GNU coreutils you can do it more efficiently:

find folder0 -type f -exec cp -t targetfolder {} +

The former version runs cp for each file copied, while the latter runs cp only once.

With zsh, thanks to ** for recursive globbing and the glob qualifier . to match only regular files:

cp -p folder0/**/*(.) targetfolder

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