  We present a classification of all spherical indecomposable representations
of classical and exceptional Lie superalgebras. We also include information
about stabilizers, symmetric algebras, and Borels for which sphericity is
achieved. In one such computation, the symmetric algebra of the standard module
of $\mathfrak{osp}(m|2n)$ is computed, which in particular gives the
representation-theoretic structure of polynomials on the complex supersphere.
