It is a three stage process:
1 Candidates for law/LSE are judged against candidates for law o decide who is admitted to read for some form of legal course. Whilst the initial decisions are college decisions, these are now moderated at university level to ensure consistency across the university. Obviously the candidates needing to be considered are the borderline "in" and "out" candidates.
2 Within the cohort of law/LSE applicants, a decision is made as to which of them is admitted for law/LSE and which for law (as there is a surfeit of law/LSE applicants the possibility of all the law/LSE places not being filled doesn't arise). This is a university decision. No college has a separate quota for law/LSE
3 The colleges decide to whom to make a standard offer and to whom to make an open offer.
Only at a college level. There is no surplus of law/LSE candidates at a university level. The university makes the "right" number of law/LSE (including law and a language) offers and at university level there are separate quotas for each language/destination. However because colleges have no separate quota for law/LSE distinct from that of law there is a random element in where the law/LSE students end up.
Law and law/LSE are unique or virtually unique in Oxford regarding subjects linked in a college quota in that the courses are of different length. It really doesn't matter very much whether a college ends up with a lots of maths and philosophy students rather than maths students provided the overall quota of philosophers across all the combined subjects which include philosophy is not exceeded. It is that potential disruption to course numbers (not only the loss of students for a year but the surplus the following year) which means that colleges (particularly the small law colleges) don't want too many law/LSE students.
Any selection of candidates for admission on non-academic grounds is long in the ancient past.
I said in my previous posting that I thought there was alack of clarity about how persons were chosen for open offers. They long post-date my time in Oxford. I speculated about this and astro67 has confirmed much of my speculation (but didn't comment on my non-academic point). A new poster, of whose background I know nothing, has flatly denied it.
The point about open offers is that acceptance decisions are not usually a matter simply for the subject tutors. The aggregate college quotas for each subject exceed the quota for the entire college. In other words the college cannot fill every place it theoretically has for every subject in any given year. Before there were open offers most colleges worked on a system that the internal quotas under the control of the subject tutors (particular for the larger subject groups in a college) were lower than the external quotas set by the university. The last few places were then reserved to an academic committee or the senior tutor or the head of the college and could go the subjects with particularly strong cohorts that year.
Open offers have rather taken the place of this. The basic idea is that open offer candidates are there to replace people who miss their grades or otherwise don't show up, but it is a lot more complicated than this because people fall ill and have to re-start the course, people change subject and various people (such as the organ scholar and any Rhodes scholars reading for a second BA) are supernumerary for some purposes. Of course the college may be called upon to honour open offer guarantees in other subjects. Yet the college might still be trying to hit an intake of 107. Accordingly, the final say is normally one for the college centrally and whilst the law dons may have decided their order of preference for which of the open offer lawyers they want (because some other college might have first pick on this college's first choice candidate), the college may be taking 4 open offer candidates but have 6 subjects wanting one. It is that last point where I was speculating that non-academic factors may end up playing a part because asking whether candidate A is a better lawyer than candidate B is a chemist, is a rather futile exercise.
The college that sent the offer.
Although of the information is on the Oxford website
http://www.law.ox.ac.uk/undergraduate/admitfaqscourse2.php regarding the university rather than the college making the law/LSE decisions, much of this is anecdotal over many years which does mean some of it may have changed. I try and revise where credible information is provided by others.