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The cash cow has grown so fat that it can barely inch forward.

That, more or less, is the state of Google’s search ad business. Its growth has almost flatlined, as marketers shift spending to mobile and other digital ad vehicles, per the quarterly Adobe Digital Index out today.

Google reports its second quarter earnings on Thursday.

Adobe backs out the numbers for its survey (since Google doesn’t give them) from around 900 billion search and social ad impressions. By its count, growth in Google’s search revenue drops in the red in the first quarter, after a holiday surge, then returns in Q2. Adobe estimated the business ticked up 4.5 percent quarterly last year; for this quarter, Adobe expects it to expand by only 1 percent to 2 percent.

The punier search engines, Bing and Yahoo, are projected to grow at higher rates this quarter. Google’s loss is likely coming from its long tail of small advertisers, who are angling for better returns, said Adobe’s Tamara Gaffney, the report’s principal analyst. “For a lot of marketers, the next best place to spend their dollars is to go outside of Google,” she said.

Of course, even if search ads at Bing and Yahoo are growing faster, the pie remains Google’s. It will claim 55 percent of the $82 billion spent on search this year, according to eMarketer. China’s Baidu comes in second at 9 percent.

Adobe’s report also unpacked some of the outcomes of Google’s “Mobilegeddon” — its move in April forcing websites to optimize for mobile devices.

Here, it appears that Google is doing what it set out to do. Traffic to websites with little mobile usage fell during the quarter and Google was able to soak more mobile money. The cost-per-click rate for mobile search ads rose 16 percent, while the click-through rate fell 9 percent; basically, ad buyers paid more for less. That may tick off advertisers, but it bodes well for Google, which has promised investors it has a solution for its nagging mobile dilemma.

Finally, the report throws some more fuel on the Facebook vs. Google ad match. In the quarter, Facebook display ads grew at nearly fourfold the rate of its foe.

Facebook comes out better in approval ratings, too. Adobe polled digital ad spenders on whether they think their ad money achieves “genuine interest” with viewers, a thing these spenders would like. Only 17 percent of those polled said they agreed with ads on YouTube; 51 percent answered affirmatively for ads on Facebook.