In dueling press releases, Vodafone and Telecom Italia announced on Tuesday that they have both signed contracts with Apple to carry the iPhone in Italy — the first sign that Apple may be relaxing its demands for revenue sharing with individual carriers in exchange for exclusivity.

The biggest deal is the one with Vodafone. Having lost the bidding war to carry the iPhone in its home market to O2, UK-based Vodafone (VOD) got its revenge with this terse, two-sentence press release:

“Vodafone today announced it has signed an agreement with Apple to sell the iPhone in ten of its markets around the globe. Later this year, Vodafone customers in Australia, the Czech Republic, Egypt, Greece, Italy, India, Portugal, New Zealand, South Africa and Turkey will be able to purchase the iPhone for use on the Vodafone network.” (link)

This is an important deal. Vodafone is the world’s second largest mobile phone carrier, after China Mobile. At the end of 2007 it had, through wholly owned and partially owned subsidiaries, the equivalent of 252 million customers in 66 countries.

Only 10 of those countries are covered by the deal announced on Tuesday, but they include some big ones. India, for example, has a population of 1.12 billion that is snapping up mobile phones at a blistering pace. The number of mobile phones in Italy reportedly exceeds its population. Piper Jaffray’s Gene Munster calculates that the Vodaphone deal nearly doubles the size of the iPhone’s available market, from 153 million potential subscribers today to 293 million once the 10 new countries are on board.

But most of the important details were missing from Vodafone’s press release. When does the deal start? Is it exclusive? Is there a revenue sharing agreement? Will Vodafone be selling first- or second-generation iPhones? (Some of the countries listed don’t have a 3G network.)

All of which made us wonder why Vodafone spilled the beans on this day, and in this way.

We didn’t have to wait long for an answer. It came in a press release from Telecom Italia (TI-A), which also announced on Tuesday that it had signed an agreement to carry the iPhone in Italy.

This marks the first time Apple (AAPL) has signed non-exclusive contracts with two carriers in the same country. European commentators are already asking whether Apple’s partners in other countries will now revolt against what some perceived as onerous terms. “This is definitely a sign Apple is capitulating,” Will Draper, an analyst at Execution told the Times of London. (link)

How many other non-exclusive deals are waiting in the wings? Probably just as many as it takes for Steve Jobs to comfortably beat his target of selling 10 million iPhones in calendar year 2008.