How many forks or veriations of ubuntu operating systems are around? [duplicate]

Check https://ubuntu.com/download/flavours for officially supported Ubuntu flavors:

Kubuntu

Kubuntu offers the KDE Plasma Workspace experience, a good-looking system for home and office use.

Lubuntu

Lubuntu is a light, fast, and modern Ubuntu flavor using LXQt as its default desktop environment. Lubuntu used to use LXDE as its default desktop environment.

Ubuntu Budgie

Ubuntu Budgie provides the Budgie desktop environment which focuses on simplicity and elegance. It provides a traditional desktop metaphor based interface utilising a customisable panel based menu driven system.

Ubuntu Kylin

The Ubuntu Kylin project is tuned to the needs of Chinese users, providing a thoughtful and elegant Chinese experience out-of-the-box.

Ubuntu MATE

Ubuntu MATE expresses the simplicity of a classic desktop environment. Ubuntu MATE is the continuation of the GNOME 2 desktop which was Ubuntu’s default desktop until October 2010.

Ubuntu Studio

Ubuntu Studio is a multimedia content creation flavor of Ubuntu, aimed at the audio, video and graphic enthusiast or professional.

Xubuntu

Xubuntu is an elegant and easy to use operating system. Xubuntu comes with Xfce, which is a stable, light and configurable desktop environment.

Other Ubuntu-based distros are at least the following:

• UbuntuDDE - uses Deepin Desktop Environment;
• Ubuntu Cinnamon - uses Cinnamon desktop;
• Ubuntu Unity - uses Unity 7 desktop environment;
• Ubuntu Web - Ubuntu web remix combines the power of Ubuntu & Firefox to give you a powerful, free/libre web OS;
• UbuntuEd - potential replacement for obsolete EduUbuntu;
• Wasta Linux - uses Cinnamon desktop and some useful applications;
• Li-f-e: Linux for Education - uses MATE, specialized in education.

If you want more - use DistroWatch.com and set Based on filter to Ubuntu or Ubuntu LTS there.