  We discuss various types of Tits Alternative for subgroups of graph products
of groups, and prove that, under some natural conditions, a graph product of
groups satisfies a given form of Tits Alternative if and only if each vertex
group satisfies this alternative. As a corollary, we show that every finitely
generated subgroup of a graph product of virtually solvable groups is either
virtually solvable or large. As another corollary, we prove that every
non-abelian subgroup of a right angled Artin group has an epimorphism onto the
free group of rank 2. In the course of the paper we develop the theory of
parabolic subgroups, which allows to describe the structure of subgroups of
graph products that contain no non-abelian free subgroups. We also obtain a
number of results regarding the stability of some group properties under taking
graph products.
