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.
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