It is worth remembering that a party or grouping of parties may be able to secure a majority even if it does not hold more than half of the seats in the House. This is because a confidence vote, like all questions put to the House, is decided by a simple majority of votes cast. To illustrate the point: a party may state publicly and unambiguously that it will not provide support on matters of confidence to any other party or grouping of parties, and that it will instead abstain on confidence votes and vote on legislation case by case. Whatever that party’s motives, its abstention is constitutionally significant, because it reduces the number of votes another party or grouping of parties will need to win confidence votes and command the confidence of the House.
This is not an impossible scenario. A centrist party could take that stance. They would effectively hold the balance of power on votes on individual legislation, but abstain on confidence and supply votes. This would mean that the party or bloc with the largest number of seats (even if not a majority) could form Government.
Since MMP was introduced, it has been the practice of the parties forming the government to commit to working together for the duration of the parliamentary term. This is not a formal requirement, and there can never be a guarantee that any agreement reached will hold in practice. My experience of New Zealanders, though, is that they place a high value on stable government, and will expect parties to make best endeavours to agree on commitments for the full term of Parliament.
This is also a key point. Parties don’t need to commit for the full term, and as the GG says, they can change their mind anyway.
It is possible for a Government to be formed without formal confidence and supply agreements. Just on the basis of a statement from a party that for now they will vote for confidence. Basically it is minority government. This is the case in Canada where minority Governments often are the case, but never have formal confidence and supply agreements.