The immigration phenomena associated with branching models have been investigated quite extensively in the past decades. In the measure-valued setting, immigration processes have been studied with different motivations by Dawson, Dynkin, Evans, Gorostiza, Ivanoff, Shiga and others. We focus on a special type of immigration associated with DW superprocesses formulated by skew convolution semigroups. Transition semigroups of the immigration processes can be characterized in terms of infinitely divisible probability entrance laws and their trajectory structures can be investigated by using Kuznetsov processes. The immigration processes provide a number of new limit theorems. In particular, the fluctuation limits of them lead to some infinite dimensional Ornstein-Uhlenbeck processes described by the branching mechanisms of the superprocesses. Other types of limit theorems can be obtained by randomizing the skew convolution semigroup.