when u taxi a char using tk, does the tk stop when b2b to an enemy char??

Hope you don't mind if I first take care of an issue of semantics. Taxiing generally refers to carrying---I only bring it up so that rulings which reference taxiing don't mess you up.

Breakaway and stopping when adjacent are concepts which only come into play when the figure in question is moving under his own volition. When being TKed a figure doesn't need to breakaway and also does not stop when passing by opposing figures.