What's the connection between Zangetsu and White Ichigo? This contains spoilers up to chapter 112 (not much of a spoiler, but still).


   White Ichigo (a.k.a. Hollow Ichigo) appeared in the Hollowfication process, when Urahara had cruelly thrown Ichigo into a pit, and he is the Hollow part of Ichigo's soul (and power). 


Now, take a look at this (this is from chapter 112, right after 


  White Ichigo first appears and gets beaten by Ichigo):


It shows not only that Zangetsu is acquainted with White Ichigo, but also is in apparently well relations with him ("sorry to have bothered you"), and is also apparently able to summon and unsummon him ("send me back already"). 

How and why is Zangetsu (a Zanpakutō!) able to summon the Hollow inside of Ichigo? Shouldn't a Zanpakutō spirit and a Hollow Spirit be natural enemies?
Both White Ichigo and Zangetsu are a part of Ichigo's being or soul. Hence, they can freely communicate with each other. The most important thing about Bleach power-ups is that they follow the basic principle of "know thyself" and thus, Ichigo himself is unaware of their true capabilities until he pays attention to them by training.