My thanks to Andrew J. Browne of Galway (my favorite city) for
responding to my question! However, I need to re-phrase my question.
And, for reference, I will include below Chapter 22 of the [Irish
Republic] Statute Number 28, of the Copyright and Related Rights Act
of 2000.

It would appear from this statute that Legal Deposits by literary
publishers in Ireland must be made with the National Library of
Ireland, TCD, the Library of the University of Limerick, the Library
of Dublin City University, four copies for the constituent libraries
of the National University of Ireland (including Galway) ... in
addition to the five copies to the BL and other libraries in the U.K.

1.) Whew! That's a lot of Deposit Copies for any literary or small
press to make! Do literary small presses in Ireland actually comply
with this requirement?

2.) I've never been able to identify at any of these other
institutions ... NUI, Limerick, Dublin ... anyone, yes ANYONE who
would agree to accept such Legal Deposits for literary/small press
publications produced in Ireland. So, if the Irish small press scene
actually complies with the requirements of the law, how do they do it?
 What names or addresses do they use to send the Legal Deposits to
these libraries?

From past experience, my distinct impression is that these libraries
don't want such Deposits, law or no law. (On the other hand, the
Library at UC Cork does seem to have an interest in collecting Irish
small press books and chapbooks ... though, is it one of the
designated Deposit libraries?)

3.) This brings us back to Peter Riley's comment that "As with
everything else, things are bound to be different in Ireland."

Sincerely,

Séamas Cain
http://alazanto.org/seamascain
http://seamascain.writernetwork.com
http://www.mnartists.org/Seamas_Cain

-------------------------

Chapter 22

Deposit of Certain Copyright Materials 198.—(1) The publisher of any
book first published in the State
after the commencement of this section or, in the case of the authority
specified in paragraph (a), the publisher of any book published
in the State, shall, within one month after the publication, deliver, at
his or her own expense, a copy of the book to each of the following—
(a) the authority having control of the National Library of
Ireland,
(b) the authority having control of the library of Trinity College,
Dublin,
(c) the authority having control of the library of the University
of Limerick,
(d) the authority having control of the library of Dublin City
University, and
(e) the Board of the British Library,
and four copies of the book for or in accordance with the directions
of the authority having control of the National University of Ireland
for use in the four constituent universities of that University.

(2) Boards and authorities taking delivery of books under subsection
(1) shall give a written receipt for every book delivered to them
under that subsection.
(3) The Minister may, on an application of a Board or authority
referred to in subsection (1), make regulations exempting from subsection
(1) in respect of the Board or authority making the application,
publications wholly or mainly in the nature of trade advertisements,
or any class of work as may be specified in those regulations,
and it shall not be necessary for the publisher of any publication so
excepted to deliver the publication to that Board or authority or for
such Board or authority to give a receipt unless as respects any particular
publication a written demand for the delivery of that work is
made by the Board or authority concerned.
(4) The Boards or authorities referred to in subsection (1) may,
before delivery of a book is made under subsection (1), request that
a book be delivered in a particular form, being one of the forms in
which the book is published and the publisher shall deliver it in the
form requested.

(5) The publisher of any book first published in the State after the
commencement of this section shall, where a demand is made in
writing by the authority having control of each of the following
libraries—
(a) the Bodleian Library, Oxford,
(b) the University Library, Cambridge,
(c) the National Library of Scotland, and
(d) the National Library of Wales,
before the expiration of 12 months after the book is published,
deliver within one month after receipt of that written demand or,
where the demand was so made before the book was published,
within one month after publication, to an address in Dublin named
in the demand a copy of that book for, or in accordance with the
directions of, that authority.
(6) In the case of an encyclopaedia, newspaper, review, magazine
or work published in a series of numbers or parts, the written
demand referred to in subsection (5) may include all numbers or
parts of the work which may subsequently be published.

(7) A copy of a book delivered to the authority having control of the
National Library of Ireland or the Board of the British Library pursuant
to this section shall be a copy of the whole book with all maps and
illustrations belonging to that book and, subject to subsection (4), finished
in the same manner as the copy in that form which is superior in quality
to any other copy in that form of the book available.
(8) A copy of a book delivered to any of the authorities referred to
in this section, other than those referred to in subsection (7), pursuant to
this section, shall be in the form specified by the Board or authority,
which shall be one of the forms in which the book has been published,
and shall be in like condition as that form of the book.
(9) Where a publisher fails to comply with this section he or she
shall be guilty of an offence and shall be liable on summary conviction
to a fine not exceeding £500 and in addition the person shall be
liable to be ordered to comply with this section.
(10) For the purposes of this section, ''book'' includes every part
or division of a book, pamphlet, sheet of letterpress, sheet of music,
map, plan, chart or table separately published, but shall not include
any second or subsequent edition of a book unless such edition contains
additions or alterations either in the letterpress or in the maps,
plans, prints or other engravings belonging thereto.
(11) Where a copy of a book requested under subsection (1) is
delivered in a form other than an electronic form, the Board or other
[2000.] Copyright and Related Rights Act, [No. 28.]
2000.
authorities referred to in subsection (1) may request, in addition to
that copy, a copy in an electronic form readable by means of an
electronic retrieval system and on such request being made a copy
in electronic form shall be delivered by the publisher to the Board
or authority concerned.
(12) For the purposes of this section, ''publication'', in relation to
a book—
(a) means the issue of copies to the public, and
(b) includes its making available to the public by means of an
electronic retrieval system,
and related expressions shall be construed accordingly.