As an analogue of the hyperbolic 3-orbifolds associated with Kleinian groups, Lyubich and Minsky introduced the hyperbolic orbifold 3-laminations associated with rational maps. They applied analogous arguments on rigidity theorems of hyperbolic 3-orbifolds to the hyperbolic 3-laminations, and showed a rigidity result of rational maps that have no recurrent critical points or parabolic points. However, even for hyperbolic quadratic maps like z2-1 or Douady's rabbit, the precise structure of its laminations have not been investigated. Moreover, even for the simplest parabolic quadratic map z2+1/4 that has a cuspidal part, its 3-lamination had not been precisely investigated. The aim of this talk is to explain the topological and combinatorial changes of laminations associated with the motion of parameter c of z2+c from one hyperbolic component to another via parabolic parameters. This method will give answers to some questions by Lyubich and Minsky about structures of laminations. We will also observe a phenomenon that is similar to "Dehn twist" of ends of 3-manifolds associated with quasi-Fuchsian groups when the parameter c moves as above.