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: tldistro@tug.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.
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 any critical post-release patches, particularly to the compiled source code. The idea is that distro maintainers can incorporate those changes without wading through all the (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 are the dockerfiles etc. used for some of our automated builds.
TeX Live contains a few programs which are not included by default as part of the TL build: Asymptote, Biber, ConTeXt LMTX (LuaMetaTeX), and Xindy. You may find it preferable to package any or all of those on their own, rather than as part of TL. There are some brief notes about them on the TeX Live build page; each is a unique situation.
Here is a list of distros and their respective maintainers, to the best of our knowledge.
Please send corrections to tldistro@tug.org.
Again, please send updates to tldistro@tug.org.