  We discuss $C^0$-continuous homogeneous quasi-morphisms on the identity
component of the group of compactly supported symplectomorphisms of a
symplectic manifold. Such quasi-morphisms extend to the $C^0$-closure of this
group inside the homeomorphism group. We show that for standard symplectic
balls of any dimension, as well as for compact oriented surfaces, other than
the sphere, the space of such quasi-morphisms is infinite-dimensional. In the
case of surfaces, we give a user-friendly topological characterization of such
quasi-morphisms. We also present an application to Hofer's geometry on the
group of Hamiltonian diffeomorphisms of the ball.
