I've turned my computer on the complicated EEZ territory around New Zealand,
by way of testing its accuracy. The three high seas enclaves turn out nicely.
Interestingly, two of them are defined by EEZ claims on islets that are
"rocks" under the UN definition, and the islets are optimistically named:
L'Esperance Rock in the Kermadecs is pretty hopeless, and the Bounty Islands
couldn't be much less bountiful! On the attached images, the EEZ arising from
these rocks is shown in a darker shade, as previously. (I was initially
intrigued that debatable rocks play such a large part in defining EEZs, but I
suppose it's no surprise. They're being claimed specifically *because* they
extend the parent country's EEZ.)
The Kermadec/North Island high seas enclave is still there, but it needs an
enlarged image to show up clearly - centred on 34 24 S 178 54 E, and about 40
sq km in area by my (*very* crude) estimate. Would be a nice place to visit,
with a yacht and a GPS receiver.
Also shown are the Australian EEZs around Lord Howe, Norfolk and Macquarie,
the latter two abutting the NZ claim.
The maps are generated as cylindrical projections (anything else defeats my
maths!) so the island EEZs are distinctly elliptical at higher latitudes.

Grant