Like most analysts, Kaufman Bros. Shaw Wu believes Apple (AAPL) will eventually end its exclusive relationship with AT&T (T) and give the iPhone to other U.S. carriers — by 2011, most likely, and perhaps as early as this fall.

But unlike most analysts, who are rooting for Verizon (VZ), he believes T-Mobile (DT) will be the next carrier to get the device.

In a note to clients, he ticks off the reasons:

• Like AT&T, T-Mobile runs a GSM network, although on different frequencies. T-Mobile’s 3G network runs on 1700 MHz and 2100 MHz while AT&T supports 850 MHz and 1900 MHz. “Interestingly,” Wu writes, “both the new iPhone 4 and iPhone 3GS support 3G at the 2100 MHz frequency.”  Verizon and Sprint (S) run CDMA networks, which would require Apple building a special iPhone.
• Apple needs another carrier to compete with Google. Google’s (GOOG) Android is still a niche product, with a 9% U.S. market share, but according to Wu it is growing strongest where the iPhone is not available.
• Verizon isn’t the only show in town. Although it is the largest U.S. carrier, with 93 million subscribers, AT&T comes in second at 87 million, Sprint at 47 million, and T-Mobile at 34 million. Says Wu: “It is notable that signing up both T-Mobile and Sprint would almost be the equivalent of signing VZ.”

Wu is sticking with his “buy” recommendation on Apple with a price target of $320 a share.

[Follow Philip Elmer-DeWitt on Twitter @philiped]