What is a university?

I've been wondering about this particularly since Lord Vader's recent musings on the necessity for us to regard students as customers and look to the economic benefit of the country. And I've been reading David Watson's new book on university morale. He offers the following interesting question (p.85). Consider the following institutions and organisations. Which is/are most like a university and in what respect(s)? (The comments are Watson's. Some of the examples might be a bit UK specific, but I hope the point is clear nevertheless.)

1. the Armed Forces (a command structure but very dependent on outsourcing);
2. the Church of England (a consensual community, but one that is legally 'established');
3. the National Trust (a private charitable society, but one which guards much of the nation's 'heritage' and acts as a tax-management device);
4. the Post Office (a 'privatized' service, with a public 'golden share');
5. Banks (private corporations, some now in public ownership because apparently the public cannot allow them to fail);
6. the NHS (a constantly restructured devolved service, where individual trusts, although nominally independently governed - especially 'foundation trusts' - can apparently be overruled or reorganized by political fiat);
7. Schools (a local authority service, but nationally regulated - including through the National Curriculum - but 'governed' on an individual institutional basis);
8. BAE Systems (a private company with a majority of public contracts).

Any thoughts? The problem seems to be that universities resemble all of these in some respect and none of them in all. But the exercise does serve, I think, to draw out some of the sometimes inchoate and potentially inconsistent ideas we might have about what universities are, how they might be governed and govern themselves, and what they might be for. (The same procedure might be followed for an Oxbridge college which is in some important ways relevantly distinct from the university.)