How to make Time Machine backups over network without OS X server? At our institute, we have several Macs (from 10.6 to 10.8) but not one is running a server version. In the one running 10.8 there are 4.5 TB of hard-drives from which 2 x 2 TB are raided together (mirrored) with to goal to use them as a Time Machine backup for all other Macs. All the Macs are connected over the institute network.

Now, how do I set up everything such that all Macs can use Time Machine to backup to this one Mac?

I've read that this might be easier when the target Mac would run OS X Server.

How is it also possible without installing OS X server?
The officially sanctioned answer: buy an Apple Time Capsule device.

Unsupported but well-known alternative: enable a hidden option that allows you to use any network drive. Open the Terminal application and run this one command:

defaults write com.apple.systempreferences TMShowUnsupportedNetworkVolumes 1

It will allow you to select any network drive from System Preferences: Time Machine. 

The network drive should be a HFS+ file system over AFP (standard file sharing from another Mac). I would strongly discourage you from using any other setup if you are not prepared to manually restore one file at a time from the backup.