Is there any paper where I can find a good explanation of the JSJ decomposition, the geometrization theorem and the relations between them when the manifold has nonempty (and non necessarily toroidal) boundary? Currently I am trying to read the original Jaco-Shalen paper and a Scott's survey paper, buy they do not look to be completely satisfactory...



Geometrization & JSJ decomposition with boundary
The work of Jaco-Shalen and Johannson actually handles manifolds with boundary. The theorem they prove (in the language of Johannson's Book) is: 


An irreducible, boundary-irreducible 3-manifold with useful boundary pattern possesses a characteristic submanifold, unique up to isotopy.


The complement of the characteristic submanifold is atoroidal and acylindrical, hence (by Thurston) possesses a unique hyperbolic metric with totallygeodesic boundary.


The characteristic submanifold has the property that every admissibly embedded I-bundle or Seifert fibered space is isotopic into the characteristic submanifold.


All the notions, including useful boundary pattern and admissible embedding, are explained in Springer Lecture Notes in Mathematics 761 (Johannson: Homotopy equivalences of 3-manifolds with Boundaries), the above-cited Theorem is Proposition 9.4 in that Book.


