Let $G$ be a real, reductive group, and let $X$ be a locally algebraic homogeneous
space for $G$ admitting a nonzero, $G$-invariant density. In this talk, we associate
to $X$ a finite number of families of irreducible, unitary representations of $G$, and
we compute the (non-empty) asymptotics of the support of the Plancherel measure
for $L^2(X)$ inside each family. In addition, we show "most" of the support of the Plancherel measure lies within these families. This is joint work with Yoshiki Oshima.