A theoretical investigation of boson versions of the t-J and t-J(z) models
on the square lattice is carried out. In the t-J(z) model, phase separation
between a hole-rich and a hole-free phase occurs, at sufficiently low hole
doping, for arbitrarily small values of J(z). The boson t-J model, instead
, features a uniform ground state at any doping for J/t less than or equal
to 1.5. No evidence of a striped ground state is found. Relevance of this s
tudy to the corresponding fermion models is discussed. Fermi statistics is
found to enhance the tendency toward phase separation: in particular, phase
separation is predicted, at low doping, in the fermion t-J(z) model, at al
l values of J(z).