Another 25 per cent of cases could be in under 12-year-olds, the paper said.
This means around 75 per cent of Covid-19 cases could be carried across the border by those not needing to be tested in order to leave.
The paper, prepared by the Covid-19 group in the Department of the Prime Minister and Cabinet, later laid bare the clear expectation of the coronavirus' spread across the country.
"By definition, the true extent of undetected infection in Auckland is not known. Any loosening of the boundary with Auckland, coupled with high numbers of reported cases in Auckland, would mean that we must expect infected people to travel across New Zealand," it said.
"In communities with lower rates of vaccination, transmission can be expected to be quicker. This means that outbreaks would be larger at the point they are detected, and harder to contain once they are detected."
The officials said pre-departure testing for everyone leaving Auckland was not feasible.
"In either case, requiring a pre-departure PCR test as well as vaccination would increase the protection, but the Ministry of Health officials advise that this would be unsustainable for more than a very limited time as demand for tests would overwhelm capacity.
"They also advise rapid antigen testing would not be suitable for use at the boundary, as testing would create significant delays if used at the boundary or be too difficult to accurately link back to the right person."