I don't think a city of more than 100,000 would be possible without a substantial amount of civil management.
Deciding with bits are for streets and which bits are for buildings needs an arbiter of som sort for starters.
If a place had a sewer it probably had a government.
Sometimes I like to recall that somewhere in Tenochtitlan there must have been some Aztec administrator doing a job like making sure the road signs are repainted every few years.
If someone tries to stop you, by what authority? If they can stop you, there's your government.
More than 100,000 people?
Even Kowloon had a degree of management by criminal groups.
Now I suppose at this point you'll move on to the next goal posts. We've been deregulated for 20+ years and we got this long list of gotchas by the statists when we did it but none of the hysterical hypothetical happened and largely because anyone capable of feeding themselves soon realizes acting in extreme bad faith in a place without police is worse for them than it is the people around them. You can add all the 'but but' whatubaut this and that but it simply isn't any more a problem than the fact we also haven't installed anti-aircraft lasers in case aliens arrive.
Perhaps if you named the place I would be more able to assess information.
I have little to go on, when you say privately owned? By whom?
Is the ungoverned nature recognised by the country within which it resides?
Similar to socialism, which works just fine in a family, or hunter gatherer tribe, but starts running into problems at large scale.
In Ireland, for as long as it has existed with its own government, the two have been pretty heavily intertwined.
Governments back then were remarkably interventionist and even kind of semi state capitalist even by modern standards.