How does size in a scan and scroll work?

I was wondering how size in a scan and scroll request works? In the latest documentation, it specifies

The size parameter allows you to configure the maximum number of hits to be returned with each batch of results.

Looking at some older documentation I found the below

Although we specified a size of 1,000, we get back many more documents. When scanning, the size is applied to each shard, so you will get back a maximum of size * number_of_primary_shards documents in each batch.

Is the above statement still true?

If true, does it aggregate all the results from each shard and return the results in batches of 1,000 on every scroll?

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