This is a Sprint powered phone and provides true LTE speeds. However, make sure you have strong Sprint native coverage in the places you want to use this phone especially if you want to take advantage of the LTE speeds. Not all Sprint coverage areas have LTE at this time but from what I hear, the goal is to have it in all their 3G areas by the end of 2014 ...that's the goal but we know that could be far fetched.
This phone only uses Sprint native coverage and will not roam so that is why you want to make sure you are in a strong Sprint coverage area.
Sprint coverage is not good compared with Verizon and AT&T so again, make sure you have good Sprint coverage in the places you plan to use this phone.
Sprint 4G LTE currently is NOT in many areas but is expanding quickly. The Sprint coverage map will not show all the areas that have LTE so even though the map may not show LTE, you may have it nonetheless. Just make sure you are in an area of otherwise strong Sprint native coverage.
For those of you who doubt this is a Sprint LTE phone, read this (copy-and-paste):
I found out on the WalMart web that the S III is a CDMA-S.