As Justiciar says, a non-equity shareholding is basically pure rental (with all that that implies legally, ANO-wise, and HMRC-wise) but the renter generally buys an entitlement to a block of hours.
This hour-block purchase creates motivation for the renter to make use of the plane - otherwise you end up with a bunch of renters of whom many end up flying too little and end up with poor currency. Been there, done that
GA is full of people who talk and talk but won't put 2p where their mouth is.
The problem to watch for anybody setting up such a scheme is that, in general, you will want to own the plane in a limited company (to protect the proprietors from possible uninsured losses caused by a renter), and the existence of a ltd co. exposes the Director(s) to an Inland Revenue (who nowadays are a bunch of crooks, targeting boats, horses and planes, in the sure knowledge that they can collect a £10k cheque easily to get off somebody's back) attack under
Benefit in Kind. Been there and done that, too
There are defences to a BIK attack but they are not all that attractive; one is for the Director(s) to not have any access to the plane (and preferably not even have a license); another is for all flyers to each own a share (which then makes it a traditional share-based syndicate); another is to be prepared to fight it through the General Commissioners which will cost you £10k just to instruct a tax barrister but you will probably win
so long as the business has actually made a taxable profit (because as I say the present-day Revenue is a bunch of bent chancers who bank on people caving in); another is to do a full advance disclosure to the local tax inspector before the scheme is set up and get his written agreement.
It is difficult to make a taxable profit (with a decent plane; with a highly utilised old wreck you can do it OK) not least because once you introduce capital allowances (note that 25% a year writedown is the max allowed on a rented-out asset) the writedown will likely wipe out any possible operating profit. Then all you need is a bunch of dodgy renters and the proprietor suddenly finds himself a pretty significant customer of the business
This in turn provides the Revenue shark (who can smell blood anywhere in his operating radius and has all the honesty and integrity of a shark) with an open door. You, being advised by a cheap street corner accountant, will have followed the
standard BIK guideline and very properly invoiced yourself for your flying at the external-customer rate, but the crook will attack this by saying that this is invalid if the "business is not set up to make a profit". And hey ho hey ho he doesn't need any more proof because he just needs to point to your Accounts which show a persistent bottom line loss. Your only way to get out of this is to show to the Commissioners that your business plan was actually valid but you failed to make a taxable profit due to unforeseeable circumstances.
I've got a feeling that the various zero-equity groups prominently operating have either done deals with their local inspectors, or they know something which nobody I came across knows, or they are fools. Or the hour blocks sold generate a lot of revenue in themselves, which is possible.