Samsung has just announced that AT&T, Verizon, Sprint, T-Mobile, and US Cellular will all get the Galaxy S III in June, though "Exact pricing and retail availability will be announced by each of the five carriers in the coming weeks," so we don't know the full details just yet. Samsung says that pricing will be "starting from $199," though whether that pricing will hold across all five carriers remains to be seen. Both LTE and HSPA+ 42Mbps will be supported, so expect all five carriers to tout their models as 4G devices.
Most notable of all, Samsung's PR says that it is "delivering the same iconic smartphone design and premium content sharing experience with AT&T, Sprint, T-Mobile, Verizon Wireless and U.S. Cellular." That statement, our earlier leak of the Galaxy S III on T-Mobile, and the fact that Samsung's PR doesn't have carrier-specific variants all lead to one conclusion: Samsung doesn't appear to be creating carrier-specific variants of the GSIII beyond customizing the radios. No silly per-carrier names like Fascinate and Epic 4G. No (It's also worth pointing out that all of the US models of the Galaxy S III will include 2GB of RAM).
Samsung had scored quite a coup with the original Galaxy S, launching variants on all four major US carriers at the same time. With the Galaxy S III, the company appears to have topped that feat by launching an identical-looking phone on five US carriers. Unfortunately, it's an open question whether or not Samsung will be releasing on all five carriers in short order; the company's PR says only that the the releases will be "beginning" in June.