I have 10 star books I had downloaded on my old phone and would like to do that on my new phone? Do I have to connect my new phone to my computer to get those books on my new phone?
If they are in iTunes Library, then that would be the easiest way - sync the new phone with iTunes. This will also transfer everything else you had synced to the old phone.
iOS- Transferring information from your current iPhone/iPad/iPod touch to a new device
Downloading past purchases from the App Store, iBookstore, and iTunes Store
Retrieving data ...