  We consider a system of Gross-Pitaevskii equations in R^2 modelling a mixture
of two Bose-Einstein condensates with repulsive interaction. We aim to study
the qualitative behaviour of ground and excited state solutions. We allow two
different harmonic and off-centered trapping potentials and study the spatial
patterns of the solutions within the Thomas-Fermi approximation as well as
phase segregation phenomena within the large-interaction regime.
