We identify all possible classes of solutions for two-component Bose-Einste
in condensates (BECs) within the Thomas-Fermi (TF) approximation and check
these results against numerical simulations of the coupled Gross-Pitaevskii
equations (GPEs). We find that they can be divided into two general catego
ries. The first class contains solutions with a region of overlap between t
he components. The other class consists of non-overlapping wavefunctions an
d also contains solutions that do not possess the symmetry of the trap. The
chemical potential and average energy can be found for both classes within
the TF approximation by solving a set of coupled algebraic equations repre
senting the normalization conditions for each component. A ground state min
imizing the energy (within both classes of states) is found for a given set
of parameters characterizing the scattering length and confining potential
. In the TF approximation, the ground state always shares the symmetry of t
he trap. However, a full numerical solution of the coupled GPEs, incorporat
ing the kinetic energy of the BEC atoms, can sometimes select a broken-symm
etry state as the ground state of the system. We also investigate effects o
f finite-range interactions on the structure of the ground state.