A.H.
Honestly, I never really went the Tivo route, so I'm not entirely sure what it is. I expect that U-verse would replace your Tivo, but you'd have to talk to the people at AT&T to know for sure. U-Verse comes with a DVR and the ability to program your shows to automatically record, as well as pause live TV (which is kind of what I thought Tivo was, but I was busy with Dish Network at the time and never did the Tivo thing).
Hope that helps.