copy paragraphs containing

I have a file containing groups of lines separated by an empty line.

In vim speak each group is called a paragraph and I can use the
following from motion.txt to move by paragraph:

*{*
{ [count] paragraphs backward. |exclusive| motion.

*}*
} [count] paragraphs forward. |exclusive| motion.

How would I find all 'paragraphs' that contain a specific string and
copy each paragraph to another buffer or register?

I know how to do it with lines:

qaq
:g /string/y A

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