Canonical models and stable reduction for plurifibered varieties
  A cheap method for constructing canonical models and complete moduli for complex projective varieties with a structure called "rational plurifibration" is given. A result about semistable reduction (whose nature is slightly different from alg-geom/9707012) is deduced.   The method involves recursive application of moduli stacks of twisted stable maps (math.AG/9908167) and a systematic circumvention of any difficult MMP issues. 
Dan Abramovich