Composing is mostly on the solitary end of a private-public partnership. Performing, recording, broadcasting is the public side. Many composers carry out their end as covertly as possible, often in near- sacred spaces, our hermitages, garretts, and ateliers. (Mostly a good thing, too: I'm not alone among my colleagues in never having gotten good marks for "gets along well with others" in grade school.) Some work privately and keep it so, other hold on to every scrap and sketch, allowing the possibility that their steps to be retraced by others (for examples, see the Elliot Carter and Roger Reynolds archives online at the LOC site)*.
However composition is often taught in institutional settings and taught to groups of people, whether in formal courses (with exercises and assignments) or in more open seminar environments (Paul Bailey usefully points to a New Yorker article about creative writing workshops, an enterprise parallel in many ways to composition instruction, which asks good questions about the value of the enterprise pedagogically and the nature of its impact on writing itself.) Typically, though, most composers who are taught in institutions get a mixture of group and one-on-one instruction. My impression is that most directed composition ends with the model compositions associated with theory sequences, but directed composition assignments in groups can be very exciting (Cage's assignments to his New School classes and Stockhausen's group projects at Darmstadt are cases-in-point).
Some composition teachers like to examine every detail in a student's work, others are most focused on the bigger picture. Personally, I don't find much value myself in having my work edited note-by-note by a teacher. Iin the end, I take responsibility for every note; another set of eyes canusefully help me with the editing, but they don't have to belong to my teacher and I refuse to be cross-examined on every detail. That said, I do value highly the exchanges with teachers that focus on getting the ideas right, and the execution both clear and polished. I was lucky to have composition teachers and fellow/sister composition students who shared that preference, but there are certainly ideal student/teacher pairs and groups who have worked and do work on a more nut-and-bolts level. (This too: Seminar groups and private lessons can run a certain risk of turning into encounter groups and therapy sessions. Having lived through California in the 1970's, I don't have much need for that myself, but if it's good for you, fine and dandy.)
Composers also, sometimes voluntarily group together as professionals and sometimes get grouped together by others.** There are a lot of good reasons for clustering or grouping — exchange and promotion of music and ideas, playing each others' work, pooling of material resources, sharing concerts and publicity — and there are also some problems (who's in and who's out of the group? what if the group falls apart, like a marriage? what if one member is more successful career-wise than others? what if you now disavow a group?). (Ron Silliman has some thoughts on poets clustering). Maybe it's wise for groups to have some form of pre-nuptial agreement, for the worst case scenarios. My own engagement with other composers around Material Press has been both personally and musically rewarding; the association is voluntary and fair— like Frog Peak in the US the publisher only earns from scores sold, not demanding the usual 50% publishers' share of license fees, and the times we get together, socially or musically have always been good. We could, perhaps, have done more in the way of promotion, but our lack of pushiness is also a matter of style.
* There are three very practical and potentially profitable reasons for saving sketches: for revising or extending your own work, as material for teaching, and as salable archival materials. I don't save my sketches, having (a) a small horror of someday being overwhelmed by them, such that I cannot do anything new and (b) some committment to the notion that there are always more than one way to create a given musical surface, with no certainty about which one is the best or most efficient way, but those are my personal quirks. I recommend that my younger colleagues carefully save every scrap of paper and analog or digital media they make: this is your work, too.
**The best/worst example of this being the minimalists, with the most curious moment happening when the dubious, but original, quartet of Young, Riley, Reich, and Glass got re-booted (the culprit seems to have been Nonesuch records which, no surprise, was making a heavy investment in Reich and Adams) with Young out and Adams in, albeit with Glass, Reich and Adams running as fast away from the label as they could...