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In this paper, we present a physics-based analytical model for nanoscale MOSFETs that allows us to seamlessly cover the whole range of regimes from drift-diffusion (DD) to ballistic (B) transport, taking into account quantum confinement in the channel. In Part I we focus on MOSFETs with ultrathin bodies, in which quantum confinement is structural rather than field-induced, and investigate in detail an analytical description of the transition from drift-diffusion to B transport based on the Büttiker approach to dissipative transport. We first start from the derivation of a closed form analytical expression of the Natori model for B MOSFETs, and show that a MOSFET with finite scattering length can be described as a suitable chain of B MOSFETs. Then, we are able to compact the behavior of the B chain in a simple analytical model. In the derivation, we also find a similarity between the B limit in the chain and the saturation velocity effect, that leads us to propose an alternative implementation of the saturation velocity effect in compact models.