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htpcero :
No adaptor included - just the SBC board with heatsink pre-installed. The only "accessory" in the box was the CMOS battery
There are a variety of addon bits and pieces available from hardkernel.com (OEM manufacturer's own site, ships from South Korea) or their various distributors e.g. odroid.co.uk, odroid.nl etc.)
I don't recall seeing anything that adapts it to "standard" ITX category cases, although I wasn't really looking - it's mostly a bunch of specific custom cases, which are pretty inexpensive. Think more along the lines of the 3rd party cases you can find for Raspberry Pi type projects.
The only one I can speak to is the VESA "backplate" which I use to mount it to the back of my TV. The H3+ is dimensionally identical to the old Gemini Lake H2/H2+, and all the mounting holes on the PCB are in the same places so I just re-used it. It's not ...
great ... just a pair of interlocking stamped metal pieces and a plastic sheet with a variety of pre-drilled holes and slots. On the other hand it's completely hidden & out of sight, and anything more robust would be rather overkill, considering how small/light the device is.
I'm running LibreELEC on it ... an `embedded` Linux + Kodi combo.
One thing to bear in mind in with that setup ... the Linux underpinning they use for the Kodi 19.x Matrix builds is only on kernel 5.10
The iGPU on the Jasper Lake requires a newer kernel version than that so I had to go for a LibreELEC development Nightly build, which are only built with Kodi 20 Nexus beta.
I faffed around for a while trying to sort out a 5.11+ kernel to drop my old Kodi 19.4 install onto, but it was looking like a lot of hassle so I just dumped the Nightly build onto the drive (after a full backup, naturally
And what do you know, I shouldn't have bothered with all the messing around - it Just Worked[tm]. Only issue with the Matrix->Nexus migration was 3 or 4 minor utility addons that were disabled for incompatibility - nothing critical that I cared about.
I haven't yet found anything show-stopping in the Nexus beta - everything I normally use Kodi for all works flawlessly.
If you are just doing 'normal' Linux install with Kodi Matrix 19 or Nexus 20 alpha/beta added as a package, then any distro with a kernel later than 5.11 should be absolutely fine.