  Suppose X is a smooth projective 3-fold of general type and |mK_X| is
composed of a pencil of surfaces with m>1. This pencil naturally induces a
fibration f:X->C onto a smooth curve C after the Stein-factorization, which is
the main objects of this article. Based on Koll'ar's earlier works, we improve
on it and try to understand the family in terms of discrete birational
invariants of the total space as well as those of the general fiber and the
base curve. The aim of this note is to build a little bit basic facts.
