[HarryT]

Originally Posted by Steven Lake

Um, you actually have that wrong, HarryT. You only have to send copies of your book to the US Copyright office *IF* and *WHEN* you file copyright on your book. (they must be physical print copies) If you don't file copyright, you're not required to send anything to their office. The same rule applies if filing for a Library of Congress number, and yes, that too also requires sending in a physical copy as well. But that's because they want to A) see proof that the book is real, B) that it's yours, and C) then have a physical copy to file on their massive bookshelves for storage and records.

OK, thanks, Steven. I realise that it's unwise to rely on Wiki to be the source of legal wisdom, but in its article on Legal Deposit it says:

In the United States, any copyrighted work that is published must be submitted in two copies to the United States Copyright Office at the Library of Congress.[18] This mandatory deposit is not required to possess copyright of unpublished works, but a copyright registration can give an author enhanced remedies in case of a copyright violation.[19] The Library of Congress does not retain all works.

I would read that as saying that the requirement for mandatory deposit is separate from the (voluntary) process of copyright registration.

The official document on the subject from the US Copyright office says:

Section 407 of the Copyright Act (title 17, U.S. Code) subjects all works published
in the United States to a mandatory deposit requirement. The law states
that the “owner of copyright or of the exclusive right of publication” in a work
published in the United States must deposit the required number of copies in
the Copyright Office within three months of the date of publication....

The document, "Mandatory Deposit of Copies or Phonorecords for the Library of Congress" is here (it's a PDF file).