There is a PDF file indicating when CD is available at
http://content.emirates.com/download...ligibility.pdf
which quite cleary details where CD will be offered and just need to check the line applicable for journey
Assuming passenger flew on EK from AKL-SYD
EK / EK-M / EK / EK line would apply for NZ - AU1 - AU2 - ASIA - DXB
NZ EK AU1 EK-M x / AU2 EK ASIA EK DXB
would seem to apply where there is stopover at AU1 ( Sydney ) and Asia ( Singapore )
which affords
CDD in ASIA / CDA in DXB
which would be consistent with no CD being offered in Sydney