Google is gearing up for an all-out assault on the mobile-phone market that will include a new, Google-branded handset and the first comprehensive Google phone service with unlimited free calls.

For the first time, a single company will control everything from the software in users’ phones to the services they use to make calls and surf the web.

The Googlephone promises to be one of the most advanced smartphones, with a large touchscreen display and a processor almost twice as fast as the one powering Apple’s iPhone 3GS. It will probably be the first phone to run a new version of Google’s Android software, codenamed Flan, offering high-speed 3-D gaming said to be as good as that of many handheld consoles.

According to Ashok Kumar, an analyst at Northeast Securities, a financial services firm, the Google-branded phone will be built by a third-party supplier, possibly the Taiwanese phone maker HTC, and will incorporate a processor from Qualcomm.