Who is the best classical pianist alive?

Depends what they are playing, my 2 cents.

Perahia, Zimmerman, Kissin, Ashkenazy, Pletnev, Pollini, Argerich, They all made their mark in the music world interpreting the giants of the keyboard. To pick which one is the best, would be like picking the most beautiful girl at the playboy mansion? Than again I would not mind being asked to do that.....

Why always this puberty like best - fastest - highest? This may work in sports but never in art!!
I agree to your above list but I think the following are missing: Hélène Grimaud, Lang Lang, Volodos, Uchida, Brendel, Hough, Lewis.......and some more.
Whether Pollini is the best depends on the music - f.e. NOBODY plays the Schumann concerto like Grimaud and NOBODY plays Tschaikowsky 1st like Lang Lang. The question if this is THE BEST is obsolete because as I said above - art is above such measures.

My vote goes to Krystian Zimerman. At least he's my favorite of those performing today. I wish he recorded more.

Check out Eldar.
He is 18 and I think he is or will be best pianist alive. Sony records put him on Sony classical but he is playing jazz right now. I saw him live at skullers in Boston with a pianist friend that trained at berkley, He said how can I ever play piano again after seeing what he can do...

http://www.eldarjazz.com/

Mark