There must be some limit because the number of the possible moves is finite. How many handicap stones the current professionals are from that limit... who knows. Apparently AlphaGo could set a better lower limit but it should play with many more pros, and start giving handicap if needed.

I wonder if Google will make it available to pros outside these official matches. It's not that Deep Blue played so much after winning with Kasparov in 1997, right? Kasparov asked a rematch and IBM refused. Deep Blue never played again.

Our computers are stronger than it now, mainly thanks to advances in the algorithms. Deep Blue used to crunch many more positions per second than the current chess engines do on standard PC. Still they're stronger. AlphaGo is running on 1920 CPUs and 280 GPUs, so either research trims down its algorithms or we wait for CPUs with 1024 cores. But at the current size they won't fit below the keyboard of a laptop :-)