In reply to mypyrex: Sounds like a land law exam question, yum yum...
Assuming a willing lender, it's easy; the trick is that legal ownership (the name(s) on the land register) can be different from beneficial ownership (=who gets what when the house is sold). BUT A and B are at risk because the lender can repossess if C defaults. And there is a cost involved because the arrangement can't be done properly without a trust deed, which should be drafted by a solicitor. If A and B are willing then either:
1. the legal title has to be held by C. C becomes sole legal owner (hang on, don't panic, it gets better), and has sole liability for the mortgage. BUT he will have to hold the house on trust so that A, B and C have whatever shares they want (presumably A and B have a third each of the value of the house, whereas C gets a third less whatever is due on the mortage). A and B would need to protect them selves by ensuring that the trust deed stated that C could not sell without their agreement (although of course the lender can).
OR
2. All three buy the house as joint legal owners. Then they mortgage the house; they need a trust deed, exactly is in method 1, because (as set out above) what they want to achieve is not equal thirds of the value of the house-less-mortgage-debt, which is what they will have if they don't set out the precise arrangement they want. I think this arrangement is less likely to be acceptable to a lender because of A and B's age.
Going back to scenario 1, then, if C defaults on the mortgage the lender will sell. Let's assume, because I can only do easy numbers, that the house now sells for £390k, the mortgage debt plus costs of sale are £75k: of the net sale proceeds (315k, after paying mortgage and costs) A and B get £130k each and C gets £55k.
Tell me if I haven't explained that clearly and I will have another go!