This paper establishes for the first time closed-form analytical limits from first-principle on the specific on-resistance, versus breakdown voltage with mobility compensation for all the currently known high-voltage device topologies: vertical DMOS, RESURF, super-junction, and thin-film silicon-on-insulator. The rigorous analytic treatment results in equations purely based on materials constants (relative dielectric constant), well-established fitting parameters (mobility, ionization coefficient), and natural constants (elementary charge, dielectric constant). The results are equally applicable to high-voltage diodes, bipolar devices and junction-FET, but the emphasis is on DMOS structures, which are the device of choice in many applications. Conduction-modulation devices (SCR, TRIAC, IGBT) are not considered here, as the inherent forward diode voltage renders those devices nonlinear at low anode-cathode voltage, making the term "on-resistance (Ron)" meaningless. The theory has been extended by many degrading mechanisms and real-life limitations and excellent agreement with reported results was obtained.