  The compactified Jacobian of any projective curve $X$ is defined as the
Simpson moduli space of torsion free rank one degree $d$ sheaves that are
semistable with respect to a fixed polarization $H$ on $X$. In this paper we
give explicitly the structure of this compactified Simpson Jacobian in the case
where $X$ is a generalized tree-like curve, i.e., a projective, reduced and
connected curve such that the intersection points of its irreducible components
are disconnecting ordinary double points. We prove that it is isomorphic to the
product of the compactified Jacobians of a certain degree $d_i$ of its
components $C_i$, where the degrees $d_i$ depend on $d$, $H$ and on the
particular structure of the curve. We find also necessary and sufficient
conditions for the existence of stable points which allow us to study the
variation of these Simpson Jacobians as the polarization $H$ changes.
