  This is the second part of a series of two papers dedicated to a systematic
study of holomorphic Jacobi structures. In the first part, we introduced and
study the concept of a holomorphic Jacobi manifold in a very natural way as
well as various tools. In the present paper, we solve the integration problem
for holomorphic Jacobi manifolds by proving that they integrate to complex
contact groupoids. A crucial tool in our proof is what we call the
"homogenization scheme", which allows us to identify holomorphic Jacobi
manifolds with homogeneous holomorphic Poisson manifolds and holomorphic
contact groupoids with homogeneous complex symplectic groupoids.
