First off, your Tivax T9 digital to analog converter only outputs in 480i, which is standard definition. You can receive digital signals with it, but you can’t record high definition from it. The digital signals will be converted to analog and you should be able to record from that signal in standard definition with many different types of devices…vhs tape, dvd recorders, computer capture cards all should work with that output.
To record digital HD channels you would need a receiver capable of HD resolution output. Most of those will be 720p, and I don’t believe any over the air signals in the US are 1080p anyway. An example would be something like this Samsung: http://www.amazon.com/Samsung-DTBH260F-HDTV-Terrestrial-Receiver/dp/B000JV6TQY You would need a HD capable TV to take advantage of these high definition signals however.
You can also get HD capture cards for over the air transmissions for your computer.
Recording to Blu Ray format gets complicated in a hurry. You can use dedicated software and hardware just for Blu Ray…like this one from LG: http://www.amazon.com/LG-GGW-H20L-Super-Multi-Blue/dp/B000Y1AFCS/ref=sr_1_1?ie=UTF8&s=pc&qid=1218310477&sr=1-1
and software from Cyberlink, Sony, Ulead or others to author the Blu Ray disks.
It is possible to produce HD video on dvds and play them on Blu Ray players, but too complicated to outline here. Look it up at doom9.net, videohelp.com, avsforums or afterdawn.
Your biggest problem is the fact you do not have a tv set capable of playing back high definition content. It was made for 480i resolution. If you want to watch HD tv and Blu Ray video, you’ll have to upgrade your set first.