Google, Inc.'s (NASDAQ: GOOG) search engine rules on the world wide web. But although Google's power seems unmatched these days, it's conquering another universe as well. Yes, we're talking about one with a much larger installed user base than all of the PCs on the planet combined: the cellphone screen.

Google's mobile search share reached 63% of the U.S. market for mobile searches in July, according to measurement firm M:Metrics. The company already has regular web search market share in the high 60% range, and continues clobbering competitors like Yahoo, Inc. (NASDAQ: YHOO) and Microsoft Corp. (NASDAQ: MSFT). Just like Google CEO Eric Schmidt has said several times, the next biggest frontier for Google to rule is the mobile market. Looks like it's making very decent progress.

Second-place in the mobile web search market is, of course, Yahoo, with a 35% market share of mobile searches in July. In terms of market penetration, where Google and Yahoo team up with partners and carriers to get in front of customers, Google has an advantage here. Yahoo! has its "Yahoo! Go" option for download on most phones (turning them into a complete Yahoo! portal), but Google's partnership with Verizon Wireless and Google's default position on the Apple, Inc. (NASDAQ: AAPL) iPhone gets it in front of way more mobile eyes. But, with only 9.2% of U.S. mobile users using search on their phones, the game is just getting started.

Google (NASDAQ: GOOG) is betting that search on wireless handsets will become a big business. The company understands that online search on the PC platform cannot grow at its current rate forever, so, at some point, revenue from its AdWords program will begin to flatten.

To combat the potential of a less robust growth environment on the web, Google is moving Adwords onto its Google Mobile Search product. The program will be free until November and ads will only run on websites designed for handset screens.

Silicon Alley Insider points to a recent survey by research firm Kelsey Group as the reason Google is so anxious to get a foothold in the new market. "Revenue from U.S. mobile search advertising will soar from $33.2 million this year to $1.4 billion in 2012."

Google has some potholes in its path. After being handily beaten in the PC-based search market, Yahoo! (NASDAQ: YHOO) and Microsoft's (NASDAQ: MSFT) MSN Live Search are working to get their products on as many handsets as possible. However, they still have the disadvantage that their search products do not produce results as good as Google's and their text ad targeting products are inferior.

In moving to the mobile platform world, Google maintains its critical edge.