  We analyze the structure of spin-1 Bose-Einstein condensates in the presence
of a homogenous magnetic field. We classify the homogenous stationary states
and study their existence, bifurcations, and energy spectra. We reveal that the
phase separation can occur in the ground state of polar condensates, while the
spin components of the ferromagnetic condensates are always miscible and no
phase separation occurs. Our theoretical model, confirmed by numerical
simulations, explains that this phenomenon takes place when the energy of the
lowest homogenous state is a concave function of the magnetization. In
particular, we predict that phase separation can be observed in a $^{23}$Na
condensate confined in a highly elongated harmonic trap. Finally, we discuss
the phenomena of dynamical instability and spin domain formation.
