TeX Live is included in a number of system distributions (“distros”). TL was originally conceived and is still distributed as a benefit of the TeX user groups, including prebuilt binaries and independent of any specific operating or packaging system, but we are glad to see it being used as the basis of the TeX installation in other systems.
We have a mailing list specifically for discussion of TL integration in distros: firstname.lastname@example.org. Feel free to post, join, or peruse the archives if you are interested.
System distributions all have their own packaging systems, so tlmgr is not used for TeX-related package updates by any distro that we know of.
If you are considering (re)packaging TeX Live, you need to carefully consider how to handle, for example, the fmtutil and updmap programs (often used directly) and hyphenation patterns (maintained via tlmgr generate language in native TL)—among many other things.
Purely as an example of two distros' choices, you may wish to peruse the Slackware build information, and the TeX-on-Debian and Debian-TeX-Policy documents. We have no opinion pro or con about Debian, Slackware, or any other distro; we're merely noting that they have written up many decisions that anyone creating a TeX distribution needs to make, for the possible benefit of anyone needing to research this.
You can get the stable TL releases as tarballs from the historic archive (under systems/texlive), which you may find easier to deal with than ISO images.,
For each major release YYYY, we maintain a branch in our source repository named branchYYYY with the most important post-release patches, especially to the compiled source code. The idea is that distro maintainers can incorporate those changes without wading through all the (exceedingly numerous) changes to the trunk. We also maintain a README.branchYYYY file with a list of the changes in the branch's Build/source/ subdirectory. The binaries in the branch are not updated; it is just a place to provide important source patches.
A list of prerequisites needed to build TeX Live is available, as well distro packages to satisfy them.
Here is a list of distros and their respective maintainers, to the best of our knowledge.
Please send corrections to email@example.com.
Again, please send updates to firstname.lastname@example.org.