Does American "condominium" as applies to building ownership have an equivalent term in British or Australian or other English dialects?

The two main types of property ownership in Britain are freehold and leasehold. Freehold means that the owner owns the property and the land it stands on. In leasehold arrangements, you buy a lease on a property for a certain number of years, sometimes as much as 999 years. That entitles you to occupy the property and sell the lease, but you don’t own the property the same way as a freeholder does. It’s often found in apartment blocks, where one party owns the land on which the property stands and the occupants of the apartments buy the lease for their own apartments and, usually, pay an annual sum to the individual or company who owns the land and, ultimately, all the properties.

There are two phrases used in England, thought the first is fairly uncommon and the other is very rare.

• Shared freehold. The owners are leaseholders with long leases, but typically each owns a share of a company which in turns owns the freehold of the property. It is similar in some ways to a US co-op
• Commonhold. A modern innovation copying some foreign forms of tenure which has turned out not be attractive

Neither have the ease of changing rules or of interfering with changes of ownership seen in US condominium House Owner Associations. So the concept of a US condo would need to be explained to most Britons who have not lived in the USA.