When you use the 1080 kit, you do the following at minimum:
1. Remove the heat sink on the GPU
2. Replace the heat sink on the GPU with the AIO cooling block (it comes with a splitter cable to power the card fan and the pump)
3. Leave everything else (the original fan, PCB heat spreader, and backplate)
Other folks have modded the 1080 PCB heat spreader to fit onto the Titan X P card. The up side is that you can mount the 1080 hybrid shroud on the card (looks nicer). The down side (at least for me) was having to mod the heat spreader and risk having something short out or not cool properly...i.e. the Titan X P heat spreader was designed to cool this card.
Keeping the Titan X P PCB heat spreader makes the card look kind of ghetto-mod-ish, but it functions very well. Both of my Titan X P cards see about 45 C during heavy use (gaming, folding @ home, etc.) (I'm getting a thermal camera for Christmas...and will take VRM/memory temperature pictures!!!)
You run the card fan at around 40% or so. This pulls air into the card and blows it across the heat spreader to keep the VRM and memory cool. The existing heat sink that you are removing was only connected directly to the GPU...it did not come in contact with the PCB heat spreader.
You have to totally disassemble the card to get at the fan connector on the PCB. Take your time, and keep the screws grouped...will take you about an hour to mod the card.
Here is a quick post I did for my cards:
http://www.overclockers.com/forums/showthread.php/776114-Build-Log-JrClocker-s-Titan-X-P-AIO-Hybrid-Cooler-Mod (I'll buy the EVGA kit when it actually comes out!)