  Spin-state transitions are the hallmark of rare-earth cobaltates. In order to
understand them, it is essential to identify all relevant parameters which
shift the energy balance between spin states, and determine their trends. We
find that \Delta, the eg-t2g crystal-field splitting, increases by ~250 meV
when increasing pressure to 8 GPa and by about 150 meV when cooling from 1000K
to 5K. It changes, however, by less than 100 meV when La is substituted with
another rare earth. Also the Hund's rule coupling J_avg is about the same in
systems with very different spin-state transition temperature, like LaCoO3 and
EuCoO3. Consequently, in addition to \Delta and J_avg, the Coulomb-exchange
anisotropy \Delta J_ avg and the super-exchange energy-gain \Delta E_SE play a
crucial role, and are comparable with spin-state dependent relaxation effects
due to covalency. We show that in the LnCoO3 series, with Ln=Y or a rare earth
(RE), super-exchange progressively stabilizes a low-spin ground state as the
Ln^{3+} ionic radius decreases. We give a simple model to describe spin-state
transitions and show that, at low temperature, the formation of isolated
high-spin/low-spin pairs is favored, while in the high-temperature phase, the
most likely homogeneous state is high-spin, rather than intermediate spin. An
orbital-selective Mott state could be a fingerprint of such a state.
