tefilla - What is the proper procedure for answering parts of Kedusha?

I checked 3 different Siddurim for instructions regarding how to respond to parts of the Kedusha. All are Nusach Ashkenaz

Art Scroll has inconsistent rules:

Weekday Kedusha Shacharit & Mincha

Cong. then chazzan say נקדש

Cong. and chazzan say קדוש together ; Chazzan only לעומתם

Cong. and chazzan say ברוך together ; Chazzan only ובדברי

Cong. and chazzan say ימלוך together

Shabbat Shacharit and Musaph Kedusha

Cong. then chazzan say נקדש

All other paragraphs are said by cong. followed by Chazzan

I don't know why Art Scroll has different rules for weekday and Shabbat. Is this an error?

Birnbaum

All paragraphs are cong. followed by the chazzan

Chayim Shlomo

For the weekday Kedusha (I haven't checked what he does for Shabbat, and, B"N, I'll edit it in later):

Cong. then chazzan say נקדש

Cong. then chazzan say קדוש ; Chazzan only לעומתם

Cong. then chazzan say ברוך ; Chazzan only ובדברי

Cong. then chazzan say ימלוך

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In summary, there seem to be 3 versions of what to do after the 1st paragraph. (All agree that the Cong. starts the Kedushah)

Version 1 - Alternate starting with the 2nd paragraph with 2nd said by Cong. then Chazan, 3rd only Chazzan, 4th Cong. then Chazzan, etc.

Version 2 - Same as version 1, except that 2nd, 4th, 6th, etc. are said by Chazzan & Cong. together

Version 3 - All paragraphs are done by Cong. then by chazzan

So, which version is correct, or are all acceptable?

Answer

The original method (dating back to the Tosefta Berakhot 1:11) which was uniformly practiced in all locations (Ashkenaz, Poland, Spain, North Africa, Yemen, Italy, etc.) is simply the leader recites the entire paragraph out loud and the congregation says the verses from Tanakh along with him (eg. "Kadosh...Kevodo"). This is the version endorsed by essentially all Rishonim through to the Shulchan Arukh and Rama (OC 125).

The Ari's practice was, for Kabbalistic reasons, to also recite the rest of the paragraph along with the leader in an undertone, and to additionally say the opening two words "Na'aritzecha veNakdishecha" aloud with the leader.

(In some places, people apparently liked saying the leader's portions along and/or doing so too loudly so he would wait for them to get it out of their systems before saying his parts, and hence the "Cong. then chazzan" instructions you see sometimes. Really though there isn't supposed to be any significant pausing by the leader during Kedusha.)