There would be untitled gentry in the same position.
Is it all private land owned by a family, not a company and is there any government land which they are using but do not own?
In the US, a single chunk of land in one holding that big would be hard to find due to government land.
IIRC, anyone know for sure?
According to the article it looks like it’s owned by a company that appears to be a family-owned business.
The Domesday book would list the ownership of some estates down to pretty much the lowest level of nobility IIRC. Some of those must still be in the original families’ possession. The Domesday Book was complied in the decade or two after the Norman Conquest of 1066 so Willy could be sure what was what and who owned it (and what taxes he could expect).
I’m trying to think of some other European countries that might have continuity of ownership - Scotland, the Thane of Cawdor and that sort of thing - almost as long. Germany, France, and some of the rest have undergone revolutions and government discontinuities, as has eastern Europe. Spain was only liberated from the Moors in 1492. What about Portugal? How about some of those tiny countries? San Marino, etc.?
Oh, and Iceland IIRC has records going back to the settlement.
It’s operated by a family company, S. Kidman & Co, which was founded by Sir Sidney Kidman (1857-1935) and is now owned by his descendants.
I don’t know whether the company owns the land, or leases or licenses it from family members who own it. Either way, I wouldn’t attach too much importance to this. The exact role played by the family company may be chosen for tax or commercial reasons, but it doesn’t affect the underlying economic reality, which is that the Kidman family own the property.
It’s also possible - indeed, likely - that the land is not held freehold, but on a pastoral lease. This form of title was invented in the nineteenth century - the government of a colony (or, later, a state) would grant land to settlers not freehold, but on a very long lease for a nominal rent. The idea was that the lease would contain terms and covenants which would control the way the land was used and developed. This was before planning codes, land use codes, etc were thought of. Again, I wouldn’t see this as interfering with the economic reality that the pastoral leaseholder owns the land any more than the application of planning codes, building codes, etc means that freeholders don’t own their land.
Multiply acreage by length of time held, and get a third answer. Obviously. 
But revolution, government discontinuity, etc doesn’t necessarily involve dispossession of private landowners - just look at the American revolution. It’s only socialist revolutions, and colonial invasions, that tend to involve this. In the past two hundred-odd years France has been through five republics, two empires, a Nazi occupation with puppet state and a couple of assorted kingdoms, but there are lots of families who have been in uninterrupted possession of the same land throughout.
What about Niihau? IIRC, it was owned by Kamehameha after he conquered it, and it’s been sold to a (short) series of private owners ever since.
The issue there is that documented possession (and documented family history) generally would be reserved for the nobility, even if they are bottom level nobility. The exception might be places like Iceland where the genealogy records do exist going a long way back.
I tried tracing my less-than-noble family back a ways, and the birth and marriage records peter out somewhere near the English civil war - the roundheads were not interested in supporting the Church of England and its “mission” to track marriages and christenings. before that, the church was only tasked with this activity IIRC about 1537 and records for the next 100 years are pretty sparse. Records for the noble families however go back much further.
The other problem is that the turmoil of war or revolution would mean that quite often records would be destroyed; so the property may have been continuously owned, but the evidence is gone. The French for example would have likely confiscated most property belonging to those with a noble title, and there may be a discontinuity in the family tree. I’m not sure what the state of church and land records would be like in, say, Italy, or even India or Thailand or anywhere else with a long recorded history. In China, for example, there’s a really good chance any significant property would have been taken by the government.
Not necessarily. I assumed the answer would be someone from the nobility, so I’m also interested in examples involving the non-titled.
Not nonsense at all. There is something call Pareto optimization, that allows us to construct a trade-off curve between parameters. From chrisk’s two examples, we can’t say which is better. But we do know that parcels of 50 acres and 400 years, or 300 acres and 100 years aren’t as good. Basically, if am example loses on both size and duration, we throw it out. We’ll be left with a curve of extremes (called a “Pareto front”). Nate Silver discusses the math in another context, although he mistakenly connects the dots with straight lines instead of concave rectangles.
From this thread we have:
Houshi Ryokan, tiny size, from 718.
Nishiyama Onsen Keiunkan, tiny size, from 705.
Gardiners Island, 13 km2, from 1639.
Naushon Island, 19 km2, from 1842.
Hohenzollern Castle, tiny size, from 1267.
Anna Creek Station, 24,000 km2, from 1872.
So, the extremes are:
Nishiyama Onsen Keiunkan, tiny size, from 705.
Gardiners Island, 13 km2, from 1639.
Naushon Island, 19 km2, from 1842.
Anna Creek Station, 24,000 km2, from 1872.
*ahem *I’d include Niihau on that summary.
Conquered by Kamehameha in 1810;
Sold to the Sinclairs in 1864;
Still privately owned by the Sinclair family;
69.5 square miles.
That’s easy! The first one is 50,000 parcel-years, the second on is 60,000 parcel-years, so the 2nd one is the clear winner!
Graphing the results, it becomes pretty clear that the overall winner will almost always be either Anna Creek Station or Nishiyama Onsen Keiunkan for whatever metric is used to calculate an overall winner. It would be very difficult (though not impossible) for the winner to be Gardiners Island, Naushon Island, or Niihau. If we use the age*years formula suggested by foolsguinea and Qadgop the Mercotan, the answer is unambiguously Anna Creek Station for 3432000 kilometer squared years, followed most likely by other large and long-lived cattle ranches such as JA Ranch.
I estimated the size of Nishiyama Onsen Keiunkan as 1 kilometer squared based on pictures online ー no exact source seems to exist.
I bet my Imperial Speeder Bike could make that run in less than 11 parsecs!