  We develop a model for the origins and redshift evolution of spheroid scaling
relations. We consider spheroid sizes, velocity dispersions, masses, profile
shapes (Sersic indices), and black hole (BH) masses, and their related
scalings. Our approach combines advantages of observational constraints in halo
occupation models and hydrodynamic merger simulations. This allows us to
separate the relative roles of dissipation, dry mergers, formation time, and
progenitor evolution, and identify their effects on scalings at each redshift.
Dissipation is the most important factor determining spheroid sizes and
fundamental plane (FP) scalings, and can account for the FP tilt and
differences between disk and spheroid scalings. Because disks at high-z have
higher gas fractions, mergers are more gas-rich, yielding more compact
spheroids. This predicts mass-dependent evolution in spheroid sizes, in
agreement with observations. This relates to subtle evolution in the FP,
important to studies that assume a fixed intrinsic FP. This also predicts mild
evolution in BH-host correlations, towards larger BHs at higher z. Dry mergers
are significant, but only for massive systems which form early: they form
compact, but undergo dry mergers (consistent with observations) such that their
sizes at later times are similar to spheroids of similar mass formed more
recently. We model descendants of observed compact high-z spheroids: most will
become cores of BCGs, with sizes, velocity dispersions, and BH masses
consistent with observations, but we identify a fraction that might survive to
z=0 intact.
