The New Zealand right seems to be quite fond of monarchical fictions about our constitution. Firstly, there's their persistent belief, trotted out every time Parliament passes legislation they don't like, that the Governor-General may refuse assent to legislation. Another, most recently voiced at The Hive, is their seeming belief that the Governor-General has some sort of "choice" who they appoint as Prime Minister:
This is election year. Most people believe that National will be the largest party in the new Parliament but only the very brave are saying that National will win more than 50% of the vote. Most people believe that the next Government will be determined by a coalition deal stitched up after the election. And it is quite possible that things will be very close in this coalition race. The Governor-General might well be confronted with a choice as to which side has formed the coalition/supply support agreement that is most likely work. It hasn't happened yet, but it could. Both Labour and National could be going to the GG to say that they can form a government. In these circumstances The Hive would rather have a totally impartial Chief Secretary at Government House rather than one who wants another three years of Labour. The Chief Secretary would be the first port of call for counsel for the GG.This displays a fundamental misunderstanding of the role of the Governor-General in government formation. According to longstanding constitutional convention (and sheer practicality), the governor-general "appoints as Prime Minister the leader of the party or group of parties that has, or appears to have, the support of the House of Representatives" (Cabinet Manual 1.17). This support can not just be claimed, as Queen Bee suggests, but must be confirmed by each party involved (4.36). So, this isn't something over which there can be uncertainty - either you have a majority, or you don't. And in situations where it is unclear, where the parties have not made it public who they will support, it is the Governor-general's job to wait for matters to become clear, rather than stepping in and choosing one side or the other as the winner.
(What happens if the Governor-General ignores convention and appoints whoever they want? The last time it happened - when William IV sacked his PM and appointed Sir Robert Peel in his place - the resulting "government" was simply unable to govern. Without a Parliamentary majority, it could not pass legislation, it could not appropriate funds, and lasted all of four months. After which it became crystal clear that the monarch (or their stand-in, in our case) simply couldn't do that sort of thing any more).
Of course, if we really wanted to end this fiction, we'd stop doing things arse-backwards in the manner of an absolute monarch deigning to recognise the people's choice, and have Parliament vote before a government is formally appointed. That way, there can be no disputing the outcome, and no question of where the support of the House lies.