www.tynetees.tv is still live, though it doesn't direct you to ITV. It instead directs you to a blog, which has seemingly only recently started. One of the blogs is about a TV fitness show.
The C3NE and the whole Channel 3 thing did show that the issue over the 1989 ITV corporate branding, where some regions would take it, such as TTTV, and others didn't, such as YTV, just resurfaced again, ironically, this time, it was the parent company refusing to use the new name made for it, C3Y, but its subsidiary did, or was forced to.
Tyne Tees had no choice but to use the C3NE logo. I liked it, and it was a novel approach to branding, but on the flip side it showed just who was in charge at Yorkshire-Tyne Tees, Of course, the licence was still in the name of Tyne Tees which is why you ended up with the "North East 3 - Tyne Tees Television" logo on screen and the rather messy-sounding "You're watching Tyne Tees Television on Channel 3 in the North East" (or similar) during announcements. Mind you all this was the work of a man who when at TV-am ordered his presenters to wear pink on air!
Andrew Wiseman actually mused on his site at the time that if the entire ITV network had adopted the Channel 3 branding then LWT would have had to be branded as "Channel 3 London (Weekends Only)".