Definitely check with INZ, but I can tell you that my first partnership visa (way back in 2002!!!) was based on time spent living with hubby (at that time my bf) and various other couples in a flatshare. Our names were on all the bills, so we had that as "proof" to send in. Two of the couples we shared with also got partnership visas, and because their names weren't on our rental agreement we wrote statutory declarations to say that they were flatting with us - they did have other official-looking post coming to them at that address though, like their bank statements and cellphone bills.
That said, all of this was in Australia. The systems are similar but by no means identical!