The relevant report "Potential long-term pathways to a low carbon economy for New Zealand", Wellington, Ministry for the Environment, August 2014, is not available from the Ministry's web page. However, I requested it from the Ministry via the 'For Your Information' website.
Incredibly, Idiot Savant had a blog post about it up at No Right Turn on Friday titled Climate change: No path to lower emissions under National before I had even updated the status of my Official Information Act request on FYI.
The paper explicitly sets out to explore a New Zealand carbon dioxide budget consistent with limiting eventual global warming to two degrees Celsius, using the contraction and convergence method.
Presumably because of that aim, the paper appears to have been completely disavowed by the Ministry for the Environment. The cover letter replying to my request at FYI states that the report is neither formal advice to the Government nor is it Ministry policy. The report has a header stating that it is 'sensitive' and 'Not Government or Ministry policy'. There is an italicised inserted 'Note' saying that Treasury does not agree that contraction and convergence is an appropriate measure of a 'fair share'.
The guts of the report are three carbon budgets (a 10th percentile, a median and a 90th percentile) based on applying contraction and convergence to one of the IPCC two degrees-consistent carbon budgets. Oddly, the working calculations and the actual budget amounts are omitted. I guess I can just make another request for them. The budgets are only presented in this graph.