I guess, for the moment, we can say it's Eteri Tutberidze.
But honestly, there's no real "go-to" coach. It's about finding the right fit--the coach that works for you.
An article on FS universe about Julia & her mother moving to Moscow - she said Julia's coach was going to be Eteri or no one: (I pulled out the quote, it's a good article but long)
http://www.fsuniverse.net/forum/showthread.php?85214-Article-about-Julia-Lipniskaya
they were only sure of one thing: if Eteri Tutberidze didn't take them, they wouldn't continue their attempts, they'd simply quit figure skating.