The only land tax proposal we have in New Zealand currently is from The Opportunities Party, which proposes a revenue-neutral tax shift away from income tax and onto land tax (0.75% land tax per year, with a shifting of the income tax brackets to reduce those significantly for everyone).

In terms of fairness, the reality is that it's actually really fair for those who have owned land for a long time, because they currently benefit disproportionately from land values going up (they don't cause the land values to rise much, but society as a whole does). The current system is grossly unfair for renters, because they contribute to society just like everyone else but don't benefit from land value increases.

Land only goes up in value because of the improvements that society makes around it, which is why land in cities is very expensive. It isn't fair for landowners to benefit from this and renters to not benefit. Of course the biggest beneficiaries of all this are the banks, but most landowners didn't work for the value of their land, so losing the value of their land is fair.

Recent buyers are the most screwed over by land values dropping, because they did work very hard for their deposit and mortgage but then without working less they suddenly lose out a lot.