oVirt is a system that scales to thousands of hypervisors, but it might be overkill for a single server, no doubt

Many of the smaller foot print distro's will run fine on qemu on a modern system. You can move up to KVM but it kind of boils down to who compiled the package for either as to exactly what you get. Basically the same.

Go to SuseStudio and make a JEOS or get a pre-made appliance from somewhere and import it maybe.

Maybe I've been unclear.
I don't need a Linux distro to be run on QEMU (as a guest): all of them will do.
I need a tiny one to run QEMU itself (as a host).

Then almost all of the prior suggestions would do. Any newish distro would run qemu/kvm usually.

Have you looked at proxmox?

I bet on your hint. But I am not looking for any distribution.
I'll give that a look. Thanks.

The point of a distro tends to help the user. You can create a one of a kind in a number of ways. Things like LFS are neat but hard to maintain for common users. Gentoo makes it easier to maintain.
Plenty of distro's offer JEOS but may be called by some other name.

I only know OpenSuse and am trying hard to build a working one. Please name the other ones.

While not many offer web services, like openSuse does, there are frameworks that can be used to create a JeOS of distributions, like Debian Live (they also offer a web service for that), which can be used to create Debian and Ubuntu spins, or Fedora's livecd-creator. On distributions like Arch, Gentoo or Slackware you can easily create JeOS versions using Bash or other scripting languages.
Of course there are also installation and deployment tools like Debian's preseed mechanism or Red Hat's Kickstart that can be used for this purpose.

Edit: And there are of course the build systems, like T2 SDE, to built complete customized distros from scratch.

since you're focusing on the qemu-kvm-libvirt stack, I would definitely recommend sticking to RHEL/CentOS/Fedora, as the distributions where this particular stack is being developed and tested. I can't even count the amount of times I've been told about a problem on ubuntu or suse, which I could not reproduce on Fedora or RHEL.

Many major distro's had and still have older basic installers. One can generally use installers in advanced mode to select the types of apps they wish to have. Some give a blanket model like workstation or server.

A web search for terms like jeos linux, minimal linux and such may help.

The jeos have been geared toward a vm client but can be used for a host.

@Uqbar: You ask for tiny distros, but haven't told us what you consider to be tiny. Just for fun I made the test and created a container with a minimal Debian Jessie installation (created with debootstrap using the minbase variant) and installed Qemu to it, which resulted in a total size of about 550MB. While not as tiny as distros like Slitaz or Tinycore, I would consider that to be reasonably small.

could u not just strip a distro back and remove parts