(ABRIDGED) We examine the fundamental scaling relations of elliptical galaxies formed through mergers. Using hundreds of simulations to judge the impact of progenitor galaxy properties on merger remnants, we find that gas dissipation provides an important contribution to tilt in the Fundamental Plane relation. Dissipationless mergers of disks produce remnants that occupy the virial plane. As the gas content of disk galaxies is increased, the tilt of the Fundamental Plane relation increases and the slope of the Re-M_* relation steepens. For gas fractions fgas > 30%, the simulated Fundamental Plane scalings approach those observed in the K-band. In our simulations, feedback from supermassive black hole growth has only a minor influence on the stellar-mass scaling relations of spheroidal galaxies, but may play a role in maintaining the observed Fundamental Plane tilt at optical wavelengths by suppressing residual star formation in merger remnants. We estimate that approx 40-100% of the Fundamental Plane tilt induced by structural properties owes to trends in the central total-to-stellar mass ratio M_total/M_* produced by dissipation. Lower mass systems obtain greater phase- space densities than higher mass systems, producing a galaxy mass-dependent central M_total/M_* and a corresponding tilt in the Fundamental Plane.
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