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In this paper, we investigate the performance of an RIS-aided wireless communication system subject to outdated channel state information that may operate in both the near- and far-field regions. In particular, we take two RIS deployment strategies into consideration: (i) the centralized deployment, where all the reflecting elements are installed on a single RIS and (ii) the distributed deployment, where the same number of reflecting elements are placed on multiple RISs. For both deployment strategies, we derive accurate closed-form approximations for the ergodic capacity, and we introduce tight upper and lower bounds for the ergodic capacity to obtain useful design insights. From this analysis, we unveil that an increase of the transmit power, the Rician-K factor, the accuracy of the channel state information and the number of reflecting elements help improve the system performance. Moreover, we prove that the centralized RIS-aided deployment may achieve a higher ergodic capacity as compared with the distributed RIS-aided deployment when the RIS is located near the base station or near the user. In different setups, on the other hand, we prove that the distributed deployment outperforms the centralized deployment. Finally, the analytical results are verified by using Monte Carlo simulations.