Cytotoxic T lymphocytes (T cells) and natural killer cells form a tight contact, the immunological synapse (IS), with target cells, where they release their lytic granules containing perforin/granzyme and cytokine containing vesicles. During this process the cell repolarizes and moves the microtubule organizing center (MTOC) towards the IS. In the first part of our work we developed a a computational model for the molecular-motor-driven motion of the MT cytoskeleton during T cell polarization and analyzed effects of cortical sliding and capture-shrinkage mechanisms. Here we use this model to analyze the dynamics of the MTOC repositioning in situations in which a) the IS is in an arbitrary position with respect to the initial position of the MTOC and b) the T cell has two IS at two arbitrary positions. In the case of one IS, we found that the initial position determines which mechanism is dominant and that the time of repositioning does not rise monotonously with the MTOC-IS distance. In the case of two IS, we observe several scenarios that have also been reported experimentally: the MTOC alternates stochastically (but with a well defined average transition time) between the two IS; it wiggles in between the two IS without transiting to one of the two; or it is at some point pulled to one of the two IS and stays there. Our model allows to predict which scenario emerges in dependency of the mechanisms in action and the number of dyneins present. We report that the presence of capture-shrinkage mechanism at least in one IS is necessary to assure the transitions in every cell configuration. Moreover, the frequency of transitions does not decrease with the distance between the two IS and is the highest when both mechanisms are present in both IS.