In my opinion, government should generally stay out of everything unless the several rational interests of the individuals aggregated are detrimental to society as a whole.
One example of this is a structural monopoly. A structural monopoly is a situation where competition is impossible or strictly limited due to the nature and structure of things. Examples include military services, judicial services, roading, water supplies, sewers, information/cable networks, power lines, airports, etc. In all these cases, having competition is very troublesome. It is very difficult to have three competing sewer systems all running up to my house, vying for my business. Having one company in one part of the city and another company in another part of the city is not competition.
Military defense is another good example, where a rational individual's best strategy is to run and hide, and the group strategy of fighting back only works as a group.
Pollution control is another good example, where individuals benefit from their acts of pollution much more than they suffer, yet suffer from collective pollution much more than their individual benefit.
The system of property rights is a collective solution that efficiently and effectively covers many (but not all) of these problems, the tragedy of the commons scenario being the classic example. Some Libertarian writers presume that property rights are a free market solution, but they are wrong. The administration of property rights and deeds of title is a collective solution that allows us to distinguish between ownership, squatting, and usage.
It is my strong preference that government should not do anything else. Government is wasteful and capricious, oppresses valuable minority viewpoints and spends billions controlling inconsequential behavior, and generally is a huge drain on societal wealth.
It is my opinion that one person (or group) controlling another is fundamentally a nasty thing. Slavery is a prime example and I'm very glad society agrees with me that forcing a black person to pick cotton for you is nasty and wrong. However, society simply hasn't taken this understanding to it's logical end yet. All government action beyond what I describe above has no morally justifiable defense (at least none that I have ever heard) and is in essence one group oppressing another, one group stealing from another, or one group dictating how to live to another.
I have a theory why this state of affairs and understanding has persisted: child rearing. In child rearing, one person must control another. Anything else would be irresponsible and end in a worse result. Therefore, we have been selected as creatures with a propensity to control each other with threats of theft (fines) and incarceration (prison time). However, there is no moral reason that I can see that such egregious and onerous control should be extended beyond child rearing, except as I have outlined above.
It is democracy itself, applied at too low a level of detail, which enables this sorry state of affairs. Democracy is the whip by which the majority oppresses the minority. Democracy, if applied only to the level of principle, upon which detailed laws could be derived and held to account, would not result in the same.
With that preface in mind, I see a lot of problems with the division of public and private entities in New Zealand.
Auckland Airport: should be public. Auckland airport is a private company, but seen by the government as a strategic asset, and so no shareholder may own more than 40% (or something like that). I see Auckland airport as a structural monopoly. For that area, there is no other practical alternative for international travel, and to create one, large swaths of land would need to be acquired, something completely impractical. The airport may also be needed for military strategy. As such, I think the Crown should own it outright.
Air New Zealand: should be private. On the other hand, I see Air New Zealand as a player in a market that takes care of itself. You can reasonably have multiple airlines competing against each other. The military can use their own jets (or co-opt them in need). We have a model for this that works very well: roads. Roading is public, whereas cars are private. With air travel, IMHO, New Zealand is completely backwards.
KiwiRail: should be private but the tracks should remain public.
KiwiBank: should be private, but the reserve bank should remain public. In this case it has been proven countless times (at least three) that the government cannot run a profitable bank. KiwiBank continues to drain public funds to stay afloat.
TransPower should be public, but the generating companies should remain private. TransPower is given legal access to put their lines across other people's private properties, and as a private company, they own those rights of way (as far as I know). Can I start a competing company? No. It is untenable to have even 2 sets of power poles strewn across the country. TransPower having a monopoly is thus regulated. Regulation is a very very sticky issue, as I have written elsewhere. No, TransPower should be public. As for how a public business should be run, that's another tricky and sticky business as well, but much more tractable.