  We use a semiclassical three-fluid thermodynamic model to evaluate the
phenomena of spatial demixing in mesoscopic clouds of fermionic and bosonic
atoms at high dilution under harmonic confinement, assuming repulsive
boson-boson and boson-fermion interactions and including account of a bosonic
thermal cloud at finite temperature T. The finite system size allows three
different regimes for the equilibrium density profiles at T=0: a fully mixed
state, a partially mixed state in which the overlap between the boson and
fermion clouds is decreasing, and a fully demixed state where the two clouds
have zero overlap. We propose simple analytical rules for the two cross-overs
between the three regimes as functions of the physical system parameters and
support these rules by extensive numerical calculations. A universal ``phase
diagram'' expressed in terms of simple scaling parameters is shown to be valid
for the transition to the regime of full demixing, inside which we identify
several exotic configurations for the two phase-separated clouds in addition to
simple ones consisting of a core of bosons enveloped by fermions and "vice
versa". With increasing temperature the main role of the growing thermal cloud
of bosons is to transform some exotic configurations into more symmetric ones,
until demixing is ultimately lost. For very high values of boson-fermion
repulsive coupling we also report demixing between the fermions and the
thermally excited bosons.
