Switching from Uverse to Direct TV streaming. I have a AT&T fiber 1gig speed. I know I will turn in all my Uverse cable boxes.

No, the coaxial cable that was used for the U-verse cable boxes is not used for DIRECTV STREAM. As the name says, DIRECTV STREAM is an over-the-top (OTT) live TV streaming service that delivers television over the internet, no coaxial cable required. Streaming devices download the directv stream app, you login with your credentials, and you are good to go. The only thing you’d need would be wireless WiFi, which comes from the router. You can also use a wired Ethernet connection To each streaming device (not required) depending on the streaming device that you get (and the connectivity that it has). 
The streaming devices connect to the outlet for power and get connected to the TV for audio and video with an HDMI cable (as did your U-verse boxes). Again, the only difference is that they are wireless, live TV is delivered over the Internet. So, no need for a coaxial cable to each TV. Even on-demand and cloud DVR are available over the Internet.

Streaming devices you’d purchase for DIRECTV STREAM are Fire Sticks, Rokus, Apple TV’s, or a dedicated DIRECTV STREAM Osprey Box which has a handy remote (similar to a cable or satellite remote you are accustomed to) and amazing speeds and reliability. 

 

Your inquiry is related to AT&T services. You can engage with their experts on forums.att.com. 😊