What is the best way to centralize logging with NLog?

Question

I have been assigned a project with a lot of poorly written code that is based around SharePoint.

It consists of about 15 subprojects, some of them being windows services, some web services, some web applications running inside of SharePoint, some being webparts and even console applications. They all run on the same server and call each other.

There are already many issues in production but they are hard to trace down.
The original developer must have been a fan of either Salinger or Pokémon series judging by his tireless effort to catch all exceptions. Unfortunately, none of them get reported or logged, ever.

My current task is to introduce logging into the whole project so I could find now-invisible exceptions, follow tangled recurring calls and have some stack traces at least. I decided to go with NLog, seeing it's active and cool, as opposed to log4net which is perfectly fine but somewhat not as fancy to my taste.

Because the components are tightly coupled, I want to centralize logging in one file so related errors don't get scattered across the hard drive. Therefore, I am looking to have two or three different log files with five or more projects writing to each of them more or less simultaneously.

What is the best way to configure NLog to centralize logging? Should I have a config file for each project, or should related projects share them? Where should I put config file to log from SharePoint webparts? Am I going to face any permission issues?

I'm using SharePoint 2007.