http://www.graduate.study.cam.ac.uk/after-applying/selection-processThere is a 'Processing Your Application' pdf file on this address shared above (being the obvious source of info on the 'After Applying' part of the admissions process).
The pdf and all the rest of the information available online (e. g. respective roles and duties of each body (the department's role being dominant in my view) and the approximate length of each stage) adds up, in my opinion, to this: the Degree Committee only considers your application once the Department has recommended to admit you (to make a conditional offer in most cases) with the Department being responsible for the most important aspect of the decision - the academic aspect.
It seems, then, that those now under consideration by the Degree Committee have jumped through the most significant hurdle in the process (subject to funding issues).
Sounds about right?
The PDF to which you provided a link definitely supports the idea that the Degree Committee stage is only reached after an applicant has been made an "initial" recommendation of admission by the Faculty/Department.
Nevertheless, the actual stages as set out on the website are far more vague on this point: I read them as indicating that the first task of the Degree Committee is simply to make sure that the Faculty has "discharged its duties properly" in terms of applications, whether or not the Faculty decided to grant them an initial offer or a rejection. On this score, all applicants would pretty much progress to the DC.
However the PDF does make it look like those who have reached the Degree Committee stage have been given an initial recommendation of admission by the Faculty (since the Department can decide not to pass an application to the degree committee and render it thereby unsuccessful) that the Degree Committee can overrule.
It states as follows:
"Offer recommended by Department/faculty?
NO - Application declined
YES - Degree Committee reviews application
Offer recommended by Degree Committee?
NO - Application declined
YES - Graduate Admissions Office reviews application" [BoGS]
That seems simple enough and yet I read earlier in the thread a poster indicate that he/she had never heard of an LLM student "not" getting to the D.C. - so one must conclude either that the process has changed this year or that it is somewhat different for the LLM compared with other degrees.
I am not entirely sure I understand the function of the D.C. in all of this in relation to the Department.
[Edited by Vari57 on Jan 11, 2017]