And it notes that the desktop version has a few minor improvements compared to the battery-powered version:
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JDS Labs does not sell desktop variant, but Mayflower does.
Would a Objective Desktop Amp + ODAC with HD800 be a match made in heaven?
That's actually a misunderstanding and a very reasonable one. The guy never actually got around to designing the ODA before disappearing from the Internets.
Note that the O2 itself has a Creative Commons open source no derivatives license, so people aren't allowed to make changes to that design. What you see some people selling as a desktop O2 is just the normal O2 (and its exact same PCB and active components) stuffed inside a larger enclosure with say point-to-point wiring inside to connect the output to a 1/4" jack or some other changes on that level.
Certainly those variants are also options, but I wouldn't get too hung up on the amp. The O2 isn't the only headphone amp at all that achieves good specifications (with imperfections essentially claimed to be beyond the thresholds of audibility other than maybe the volume control channel imbalance at low volumes). In fact, higher performance DIY options even exist, which shouldn't be surprising if you look at the O2's very simple parts list and schematic, not to mention other commercial offerings, if that's what you're gunning for.