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We present results from direct numerical simulations of flows in spherical and oblate spheroidal shells, driven both by precession and thermal convection, with Ekman number
, non-diffusive Rayleigh numbers from
and unity Prandtl number. The applied precessional forcing spans seven orders of magnitude. Our experiments show a clear transition between a convective state and a precessing flow that can be approximated by a reduced dynamical model. The change in the flow is apparent in visualizations and a decomposition of the velocity into symmetric and antisymmetric components. For the flow dominated by precession, some parameter combinations show two stable solutions that can be realized by a hysteresis or a strong thermal forcing. An increase of the Rayleigh number at a constant precession rate exhibits established scaling properties for the heat transfer, with exponents
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