  We investigate a harmonically trapped two-component Bose--Einstein condensate
within the miscible regime, close to its boundaries, for different ratios of
effective intra- and inter-species interactions. We derive analytically a
universal equation for the density around the different boundaries in one, two
and three dimensions, for both the coexisting and spatially separated regimes.
We also present a general procedure to solve the Thomas--Fermi approximation in
all three spatial dimensionalities, reducing the complexity of the
Thomas--Fermi problem for the spatially separated case in one and three
dimensions to a single numerical inversion. Finally, we analytically determine
the frontier between the two different regimes of the system.
