I have tried to aggregate key thoughts into one place. It is lengthy as a result so I hope it does not put people off (if you can't cope with a long student room post humanities at Oxbridge may not be for you but you can skip down to the summary if pushed for time/attention span!). My parents tell me you put the summary/conclusions first in business for just this reason...but not in history so tough!
Pre-interview: shortlisting, first pooling/reallocation
Departments rate and group applicants (scores, quantiles), set testing policy/scoring rubrics (including adjustments for school quality/postcode deprivation in line with university guidance), set minimum qualifying score to interview, set ratio of applicants per space for each college to broadly follow, guide college on the % of applicants per quartile within their interview pool and work with them to fill/reallocate from their pool.
Colleges decide how many spaces in what subjects for final students (based on staffing), usually setting an overall target for e.g. History inc. joint honours though colleges with specific skills e.g. History of Art tutors may also set a guaranteed/minimum target at their discretion for that. In humanities I think colleges tend to get final say on who they interview/pool but are expected to meet the total pool and candidates by quartile guidance from the department meaning they cannot just stack Eton/Charterhouse/Westminster/Harrow/St.Paul's/children of staff/alumni/donors even if they wanted to (and they don't!). Colleges can decide whether to interview someone below qualifying score for exceptional reasons.
After interview: Offers, second pooling/reallocation
Department again set the cut-off score for offers, indicate which colleges they want to make open-offers (normally a college with more qualifying students than places, the department sets the criteria for an open offer - normally student needs to be strong enough to have got an offer from all/most colleges - but in humanities think the offering college makes the final decision. Having now met a couple of others who went through this like me it seems in practice if not intent being reallocated at interview increases your chance of being one of the 5-10% open offer recipients. Offer pooling//reallocation also varies between science/humanity in department/college balance but ultimately all departments seek to ensure the 'highest rated' applicants receive offers even if that means reallocating them with agreement of the colleges with 'excess' strong candidates to (presumably grateful) receiving colleges.
The exact process may vary by subject and college but the goal is shared and it always seeks to put academic potential at the heart of the decision. In some subjects it may be possible for colleges to be more muscular in making their own choices. In my experience some colleges/student guides at interview hint at this. Others/departments hinted the opposite. I was one of 5 getting offers from my school at five different colleges, our best in a decade, and when we compared notes it seemed we all got, or at least perceived we got, slightly different versions. Not quite the X-files but the truth is out there...somewhere.
There are other wrinkles. As noted sciences are mainly more centralised as more teaching is done at a departmental level but not necessarily uniform across different subject. There is sense in the difference to humanities where there is more reliance on tutorials/college relationships. Some students will get unconditional offers if results are all known. This is attractive to departments/colleges for the certainty factor but they also worry about gap students losing focus/forgetting stuff so it is still a minority of total offers given. Those of who apply in A-level/IB/other year are not disadvantaged.
Similarly some deferred students take up some places/free-up others with some year on year volatility. Colleges in humanities offering single and joint honours have discretion on the offers they make (they can pick the best irrespective of subject within an an area) but university wide it tends to average out to be fairly stable...though in History Ancient & Modern I believe 2015 was 19 offers and 2016 interview round (Oct 2017 admission) it was 29 so there is likely to be some volatility as a result in smaller joint honours courses. This risk is offset for applicants as a proportion of people applying for joint honours get offered for single honours, mainly the primary but sometimes the secondary subject...about 5% of total offers last year for history/joint honours as an indication.
After results: Final admissions
When results come in both departments and colleges can see if there is an excess or shortage of overall students meeting the grade for particular subjects/colleges. Successful students have offers confirmed.
Open offer holders have their offer confirmed and may see a sane-day UCAS code change showing they've been reallocated but can face an uncertain couple of days (me!) waiting for definitive e-mail/phone confirmation that their underwriting college has kept them (this could be improved!!!!!). Again there is a multi-step process for this e.g. Biochemistry outline a 9 step approach that can be summarised more simply as can simply be kept by offering college if they have a space, then others who made open offers (you can take someone else's ahead of your own), then colleges with spaces, then other colleges and then back round and finally back to the offering college who have to admit if nobody else takes them. This feels over-engineered and I'm told anecdotally it is simpler in most humanities subjects with a short window for a college to make a claim pre UCAS results day (as they know before we do) or defaulting to the offering college but file under 'gossip' not fact.
IF there are still gaps at certain colleges they may (with departmental discretion) reconsider students who just missed the grade but that is not common (best just make the grades!!) as they may just admit one fewer student for one year.
This is a personal aside/rant so skip if bored
Cambridge operates a small summer pool to assist with this but Oxford uses Open Offers as discussed. I think the Cambridge method (slightly modified) might be better writing as an Oxford open offer recipient! It is an odd situation to find yourself in as you've lost any control of your own destinity but still have an illusion of clarity that could then all change after the results are processed. As an applicant I found it the worst of all worlds and it dimmed my joy in my offer and somewhat (obviously not drastically) affected my studies until I had a chance to re-group/re-focus at the end of term. If you don't absolutely 'know' the college a guaranteed place at Oxford/Cambridge and a summer pool process is best as you can 'park it' mentally fo after the exams without trying to understand the complexities. It is my view that open offers increase certainty for colleges but at the expense of applicant well-being. Ultimately as an applicant you get over it and get on with it (or get in a huff/decline it) but I'd love to see ths changed to a more student-centric process. Rant over!!
Summary
Oxford seems to have multiple processes with nuanced differences working within a single shared framework of key activities, policies (diversity etc.) & dates set centrally by the university and tests, scoring set centrally by the department. Based on friend experience Cambridge is more decentralised again with colleges uptimate arbiters of offers, pooling across the board (but Cambridge students/colleges can confirm or correct this).
This is part of the 'history/charm' and it does help ensure tutors 'buy-in' to their student intake in humanities but I do think it may be one barrier among several to potential students without strong school, family/friend support to help navigate and prepare. The process may well, despite the many reforms, still be a contributing factor as somebody above suggests in dissuading applicants from certain ethnic and social backgrounds. The universities have more data than is publicly shared and may have a view or may conclude they need to do more to get a view. They shied away from completely central admissions in a relatively recent review and it wasn't just stubbornly clinging to old habits. There are valid reasons as I've tried to highlight.
Conclusion on the process(es)
The colleges may not like my assessment but I personally think if the data suggests admissions process (andperhaps more importantly the ethnic/social diversity of admissions staff & tutors) is still a factor in impairing diversity/poorer students from applying the push for uniform central admissions will be impossible to ignore. In my judgement it will be impossible to convince politicians and public they are doing everything to level the knowledge/preparation playing field otherwise.
I hope this helps and I apologise for the length but it IS complex! Right at the death I am tagging in @BrasenoseAdm again (sorry for the evening shout but it can definitely wait for another day!!!) as they can correct all my misunderstandings at leisure whilst avoiding the politics of whether/not to centrally admit.
Back to the Oxford essay grindstone!