There has been a lot of speculation about the possibility of QF becoming a member of Star Alliance through SQ buying the BA parcel of QF shares. Although, this has some potential in the business sense the logistics of dis-entangling QF from its One World partners would be enormous. QF is operating from BA's Terminal 4 in LHR and is about to move into AA's terminal in LAX which has been extensively renovated. The JSA with BA has been in service for a number of years now so there are joint facilities such as Sales Offices, Terminal Lounges etc all around the world. Computer systems have also been developed jointly and thus are "entwined". To extract an airline from this situation would be very expensive (and commercially disadvantageous as it would take staff expertise away from the core tasks - as happened when TN was integrated into QF)
As Air NZ has been in Star Alliance for a shorter time than QF has been in One World (founding member), then I believe that Air NZ has not yet spent as much on joint facilities as QF has and is less "entwined". Therefore, I believe that BA will retain its shareholding in QF and, if QF does take a significant stake in Air NZ, then Air NZ will move to the One World alliance