The concept of assembling is very simple, contributors submit a specific number of copies of their work to a central editor who in turn collates one copy from each artists' submissions into the final 'assembled' product, the number of artists submitting work defining the number of pages in each assembling. The presentation of the final magazine varies, some have loose covers inside of which the pages are placed, some are stapled together, others are bound and a number of others have been placed in a variety of different containers. Assemblings are a particularly unique concept which attempted to resolve a number of issues during the late '60s to early '70s, and its surprising that it has received such scant attention in the writings on artists' publications throughout the period under discussion.
The little documentation there is on the introduction of the assembling technique into artists' self publishing activities gives no authoritative clues as to when and who first utilized this method. Confounding this lack of information are writers who refer to the 'assembling aesthetic,' but are quite unspecific as to whether they mean assembling in the sense that everything that was sent for submission to a magazine was included (i.e. the magazine was assembled from all of the submissions), or whether they are talking about an assembling magazine in the definition I have given above.(1)
So for the moment I can only conclude that the first assembling magazine made up of multiple submissions from contributors was the magazine Notebook, compiled from 69 contributors and coordinated by Dana Atchley in Canada and completed at the end of 1969 and early 1970. (2) This same year (1970) saw the first assembling publication in the United States, edited by Richard Kostelanetz and Henry Korn, called appropriately Assembling. As one of the better known assembling magazines, and with the concept disseminated in Kostelanetz's prodigious writings, it came to serve as a model for further developments in this field. Since that time assemblings have flourished as an important international self publishing activity with approximately nine new assembling projects starting yearly from 1968-86. (3)
Assemblings represented another in the continued attacks during this period on established artworld power structures, in this case the power invested in what Kostelanetz terms the "...editorial/industrial complex..." Assemblings completely inverted the prerogative of editorial authority, and represent a decisive shift in the role of the editor to that of collator or compiler.
Some of the key points in this new self publishing paradigm can be summarized by the following:

• Assemblings provided a means for artists to publish experimental work for which there were no established outlets.
  
• Assemblings represented an 'open system,' or a participatory democracy in which editorial control was shifted away from a central authority and onto the participants themselves.
  
• Central to the concept of assemblings was the element of diversity. In the following passage Kostelanetz characterizes the work submitted to the first issue of Assembling, "...visual poetry, verbal poetry, abstract photography, playlets, minimal poetry, verbal collage, stream-of-consciousness narrative, representational graphics, picture-accompanied words, scenarios for happenings, sculptural documentation, personal journal, aesthetic manifesto, etc.." (4)
  
• Assemblings develop as unique forms of collaboration, and over the years become increasingly international in character.

Nine years later in 1979 Pawel Petasz from Poland would extend the assembling aesthetic one step further with his Commonpress, in which each issue was to be compiled by a different editor. As of 1992 approximately 64 issues have been executed (some still awaiting completion).
By way of a footnote to this section, and in answer to the question of where the idea of assemblings came from, I have to hesitantly conclude that at some point this technique crossed over from the science fiction community to the art community (further research in this area is needed). Coupled with the rise of science fiction fan clubs was the formation of amateur press associations or alliances (APAs), and to quote Fredric Wertham in his books on fanzines:

These are organizations where people send out fanzines through a central distributor. A fanzine distributed by an APA is called an apazine. The first fan APA was founded in the mid-thirties. The members send their copies to a CM (Central Mailer) who collates the copies, staples them under one cover, and sends them to every member in what is called an mig (mailing). The CM is also called an OE (Official Editor). (5)

Bibliography
Ashton, Dore. "New York commentary." Studio International, England, 175(900):272-273, 1968.
Review of Aspen Magazine (#5/6) edited by Brian O'Doherty, and S.M.S. (#1, 1968), edited by William Copley. Both of these are assembling-type publications presented as boxes containing original intermedia contributions from a variety of now well known artists.

Crane, Michael. "The Spread of Correspondence Art." Correspondence Art. Michael Crane & Mary Stofflet, eds. San Francisco: Contemporary Arts Press, 1984.
Assembling, Ovum, Hexagano & VILE (#7, Stamp Issue), mentioned in brief passage on assemblings. "In an assembling-type publication, each participant becomes editor and publisher by sending a specified quantity of pre-printed pages to central point for collation, binding and distribution."

Friedman, Ken. "Notes On The History of the Alternative Press." Lightworks, (8/9):41-47, 1977.
One paragraph on the early assembling magazines such as Amazing Facts, Omnibus News, Space Atlas, Assembling, Orgon, and Ovum.

Friedman, Ken. "Mail Art History: The Fluxus Factor." Flue, 4(3/4): 18-24, 1984.
One paragraph mention of early assembling magazines in relation to Amazing Facts Magazine, published by Fluxus West in 1968, a magazine put together loosely on the assembling principle.

Kostelanetz, Richard. "Why Assembling." The Publish-It-Yourself Handbook: literary tradition & how-to. Bill Henderson, ed. Yonkers: The Pushcart Book Press, 1973. 83-94.
Established and edited by Kostelantez and Henry Korn, this article gives a good overview of why they started Assembling, and the material they received and problems inherent in editing a magazine of this sort. This article covers up to the third issue. "Somewhat influenced by a beautiful German book called Omnibus (1969), we hit upon what we think is the most appropriate structure for a cooperative self-publishing channel. In brief, Assembling invites writers and artists whom we know to be doing unusual work, which we broadly characterize as "otherwise unpublishable," to contribute a thousand copies of up to four 8.5 x 11-inch pages of whatever they want to include."

Moore, Barbara & Hendricks, Jon. "The Page As Alternative Space: 1950 to 1969." Artists' Books: A Critical Anthology and Sourcebook. Joan Lyons, ed. Rochester: Visual Studies Workshop, 1987.
One paragraph mention of assemblings. "Another economic short-cut is to have each artist in an anthology actually produce his or her own page in the requisite number of copies for the edition, in a predetermined size. An early example of such an "assembling"-type work is Eter, which was coordinated by Paul Armand Gette beginning in 1966 in Paris. Not all of the issues used this method of publication, but under somewhat different titles (Ether, Eter, Contestation, New Eter) the magazine continued publication into the early seventies."

Perneczky, Géza. A Háló. Budapest: A Héttorony Könyvkiadó, 1991.
One section of this book is devoted to assembling magazines under the title, 'The Omnibus and Its Passengers.' At the end of this book is a synopsis in English of this chapter, and also a checklist of issues of Commonpress realized and others in progress. "The editorial method of "assembling" was favoured primarily by the adherents of mail art, who preferred to see "loose diversity" rather than the individual merits of the works, and for whom "mass effect" was a priority."

Phillpot, Clive. "Art Magazines and Magazine Art." Artforum, XVIII(6): 1980.
Short mention of early '70s assembling magazines. "In the early '70s the L.A. Artists' Publication, Assembling, and the Ace Space Company's Notebook 1 and Space Atlas exemplified an approach to magazine making whereby virtually anything was included, provided contributors submitted 200, or 500, or whatever number of copies of their work that was required to make up the predetermined size of the edition. Among the offset, mimeoed, or Xeroxed contributions were many that were intended as multiple printed artworks. These magazines were open to almost anyone who felt like contributing, and their editors pared their role down to little more than coordinators."