It is the JVC HM-DT100U.
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This VCR is, as far as I know, the only VCR with a built-in tuner sold in the USA that records everything that ATSC can offer, including 720p, 1080i, and even Dolby Digital 5.1 surround sound. Of course this requires digital VHS tapes (D-VHS). Although you could also use SuperVHS tapes too, there would be a very short recording time in comparison. It has both analog and digital HD outputs, including optical surround and HDMI--incredibly rare on a VCR in 2005. AFAIK, only two VCRs had actual 5.1 surround output signals even though many more had surround-capable connectors.
Like most D-VHS players, it has Firewire in/out. This was an interesting feature and in fact I used it on the D-VHS I did have back in the day, the much cheaper JVC HM-30000U. You could hook it up to other digital tuners to make recordings from them--not just OTA either, but also some satellite tuners and I think even certain cable tuners. You could hook it up to a PC and copy tape recordings to MPEG2 files, hence offloading perfect digital copies to a spacious hard drive to free up tapes. Or, bizarrely, you could do the reverse (copy MPEG2 stream files from the PC to tape). You could hook it up to digital camcorders to make perfect digital copies either way, etc. etc.
It is also a very premium VCR that has JVC's best technology for picture quality. I can't remember all the features any more, but it has the best motors, tracking correction, frame correction, etc. It does 480p up-scaling for standard VHS tapes, similar to how "progressive scan" DVD players improved the picture for digital TVs. It even has calibration controls for tweaking various aspects of the picture, something I've never heard of on any VCR.
All of that is fairly unique, but by far the coolest feature was the digital archive navigation. The metadata for all of your recordings was kept in onboard memory on the VCR, with indexing on each tape. This is a bit hard to explain, but the VCR kept track of every show you recorded, including which tape it was on and where it was on that tape. So you could see your whole recorded library in a digital guide, kind of like a DVR. The tapes were numbered, so you would know which tape it was on. You could insert that tape, and the VCR would use a high-speed motor to fast forward to the exact point where the show would be and start it. Gone were the days of trying to write every show on the little label, or trying to keep track of which shows were on which tapes. Gone were the days of FF/RW manually to find where the show was on the tape.
It also bucked the trend of VCRs in the later years being made very flimsy and cheap. It was solidly built and made from good materials and good techniques. They had to--it cost $1500 in 2005, a time when people had stopped buying VCRs and were switching to DVDs and DVRs.
I have to admit that I hesitated to answer you in a thread where people have nostalgia for VCRs. These only come up on Ebay a couple of times a year and there are often just 1 or 2 bidders--and so I feared that I'd be adding additional bidders that would compete with me. But honestly, at this point I've given up on buying one and now only monitor them to marvel at how they've held their price. I have sold my D-VHS player and all of my last remaining D-Theater titles and D-VHS tapes. As neat and unique as it is, I'm simply not going to get back into VHS at this point.
I hope this was a good read for some people.