a paper to get the high complications
Your AD will put your name on it, a reason why you should get a certain Patek and if you have one or more Patek he'll put these watches also on that paper.
The purpose is to know if the person who's asking for this 'special piece' is a real collector or a flipper. If you're a flipper you won't get it. If Patek once gave you one or more special pieces and they know you sold them asap ( they can see the serial numbers on auctions houses, you probalby won't be able to buy another sought after piece
A lot of people think only the clients with already several Pateks will get the hard to get pieces. THIS IS WRONG. The relationship with your AD is imo the most important. If your AD can convince Patek you're a good guy without a huge collection you also have a big chance to get that special piece.
Now, what are special pieces ?? The repeaters and the tourbillons I guess. But I was also told the Advanced research series + the limited editions + hot pieces like the 5070P were 'appllications' pieces. I can tell you the 5070R wasn't one