Every republic and every country is different and the best way forward for New Zealand is a New Zealand-style 'parliamentary republic'. This involves taking what we have and making it better. Building on the work of past New Zealanders to maintain stability and increase democracy.
A foreign UK head of state is no longer needed and we can transition the current role of Governor-General into a democratically selected, properly independent office. The current reserve powers and responsibilities would remain much the same but would be set-out clearly in legislation. An MMP parliament would remain responsible for governing the country and the Head of State role would continue to play both a symbolic and diplomatic role. The office will symbolise the continuity of the state over and above the government of the day and no one would be in any doubt that New Zealand was a sovereign and independent nation in the South Pacific. The Treaty will remain and we will still be an important member of the Commonwealth with strong ties to the UK.
By contrast the United States is a vast presidential republic with an Executive Head of State who has the power to effect legislative change throughout all American territories and possessions. Clearly this is not the way forward for New Zealand. The Republican Party in the USA is trying to work out what it really stands for and there are a multitude of people throughout the USA working to reform the whole way their political system works.
So, don't let anyone point at Donald Trump, Ted Cruze or Hillary Clinton and claim that is what New Zealand will end up like. We are not the United States and no one in New Zealand wants to emulate the American political system. New Zealand is unique and our republic will be defined by the needs of contemporary New Zealand not by someone's vague idea of what a republican is.
It is all about doing what is best for Kiwis and doing things our own way.