Polymer topology matters with respect to the structure, packing, and dynamics of chains. Herein we investigate the impact of polymer architecture on the crystallization under rigid confinement provided by nano porous alumina. We employ two poly(ethylene oxide) (PEO) star polymers and study the effect of (i) end groups and (ii) molecular weight on polymer crystallization in the bulk and under confinement. Functional end-groups have important consequences on the bulk crystallization process. Bulk end groups reduce the crystallization/melting temperatures and the corresponding equilibrium melting point. Remaining catalyst in the polymer increases the nucleation density in the bulk. Under confinement, the role of catalyst is to enhance the propensity for heterogeneous nucleation, especially in the larger pores. In the absence of catalyst, homogeneous nucleation prevails as with linear PEOs. Long-range dynamics pertinent to star relaxation are affecting the homogeneous nucleation temperature. The homogeneous nucleation temperatures for the star polymers agree with that of linear ones provided that the arm molecular weight is used instead of the total molecular weight. On the other hand, the segmental dynamics speed up on confinement.