Don't worry, I am not interested in creating a fork of a Linux distro for public use, this is more an academic question.

CentOS for example is a fork of RHEL. CentOS strips all trademark stuff, changes wallpapers and has it's own repos.

Technically speaking, how would you create a fork? Would you start with the Install disk ISO and some how change it on the disk, or would you start with an already installed system and change wallpapers/pointers to repos then some how create an install disk from it?

Are installers for systems like RHEL or Mandriva etc... GPL so that you can use them, or does a distro like CentOS create it's own installer. I know these questions are kind of broad, but I have just always wondered what the technical process of forking a distro is.

Speaking from my own experience, and I am by no means done yet, I have my own machines set up exactly how I want them. I then use LiveBuild (a set of scripts from Debian) to build it from scratch using my modifications.

That looks like an interesting tool. I wonder if Ubuntu started out with using LiveBuild? Are there any other ways that people know of.

LiveBuild is only new but it is based on LiveHelper which was in Debian Lenny at least maybe earlier. I really don't know how Ubuntu started doing it but I would assume they just used a modified Debian Installer.

Using tools like LiveBuild, Remastersys, ... is technically not making a fork, but a respin or remix, since you still use the original distro's repositories and packages. To make a fork you have to use your own, independent repos and packages.

As I understand it, if you want to do a fork, take the packages that you want to have in your distro by default and set up a repo with them. From that point on you yourself (or your team of developers/maintainers) are in charge of patching the software, building packages with newer versions and add new packages to the repo.
CentOS may not really fit into that definition, but that is because their specific aim is to compatible to RHEL.

You haven't used LiveBuild then have you? You can use your own repositories and 3rd party repositories. You do not have to use Debian repositories at all if you don't want or need to.

So, in this example of not using a tool like the ones mentioned, how would you create a copy of a distro with different wallpapers/different software installed etc...?

Would you start with an installed system, install all software that you want, and remove anything that you don't want, change the wallpaper, change the repos, then do what? Make an ISO of your installed system and somehow write an installer to add everything to another computer? Sorry if this question seems vague, but I have always wondered, and I might even want to try it on my own computer, just for the educational aspect of it.

That would be one way to do it. Since many of the remastering tools and live-installers are open-source and configurable it is not really that hard to adapt them to your needs.
Another way would be to use a normal installer from a different distro, like Debian's installer or Red Hat's Anaconda. Repackage the software that should be installed by default so that way that your changes are already integrated. Make packages of your themes, wallpapers, whatever, then create an install medium from the packages.