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This paper presents a comprehensive, numerical model for the remote Coulomb scattering (RCS) in ultrathin gate oxide MOSFETs due to ionized impurities in the polysilicon. Using a nonlocal screening approach, the model accounts for the static screening of the scattering centers produced both by electrons in the channel and in the polysilicon. Electron mobility is then calculated using a relaxation time approximation that consistently accounts for intersubband transitions and multisubband transport. Our results indicate that neglecting the screening in the polysilicon and making use of the Quantum Limit (QL) approximation can lead to a severe underestimate of the RCS limited electron mobility, thus hampering the accuracy of the predictions reported in some previous papers on this topic. Using our model, we discuss the oxide thickness dependence of the electron mobility in ultrathin gate oxide MOSFETs and the possible benefits in terms of RCS limited mobility leveraged by the use of high K dielectrics.