If I am making a p2p file sharing application, I need to know how many regular home computers must I replicate a file on for it to be ALMOST ALWAYS available. Any idea?
It is very hard to evaluate, because it is not only a question of being awake, it is also a question of being reachable and of workload capacity and bandwidth. It is not because a PC has the file and that's it is online that it will be able to deliver the file (especially if it is a big file).
This kind of info is impossible to guess from a theoretical perspective. The best approach is to measure it from your live system. But, if you really need some estimation, an average user would open its PC between 7-9 AM and shut it down between 20-23 PM, with may be a couple of hours off during the day.
You may want to Google about P2P CHURN. There is some theory out there that could help you create some model, but honestly, in my experience, there is nothing like concrete/real data.