  The normal forms associated with holomorphic systems are well known in the
literature. In this paper we are concerned about studying the piecewise smooth
holomorphic systems (PWHS). Specifically, we classify the possible phase
portraits of these systems from the known normal forms and the typical
singularities of PWHS. Also, we are interested in understanding how the
trajectories of the regularized system associated with the PWHS transits
through the region of regularization. In addition, we know that holomorphic
systems have no limit cycles, but piecewise smooth holomorphic systems do, so
we provide conditions to ensure the existence of limit cycles of these systems.
Additional conditions are provided to guarantee the stability and uniqueness of
such limit cycles. Finally, we give some families of PWHS that have homoclinic
orbits.
