Air NZ finally posted their rules and it's not good:
Its Star Alliance's 5th birthday, so we're making 5 the lucky number for Air Points members over the next few months. Fly First or Business Class with 5 or more different Star Alliance airlines in 55 days and you'll receive an additional 55,555 Air Points! This offer is valid for all sectors flown from 14 June to 7 August 2002 inclusive.
· To qualify for this special Star Alliance birthday present, you must be an existing Air New Zealand Air Points Member as at 14 June 2002.
· Please note that Air Points Members are only eligible for one award of 55,555 Air Points regardless of how many sectors are flown during this promotion. Your Air Points will be added to your account four - six weeks after 7 August 2002
· In the case of codeshare flights, the sector is eligible for this promotion when the operating airline is a Star Alliance member. The operating airline is the one which will be counted towards the 5 different airlines.
· Only sectors travelled in First or Business class are eligible for this promotion, and must be ticketed passengers. Upgrades and Award (redemption) flights are not eligible.
http://www.airnz.co.nz/travel/frequentflyers/index.jsp