We study half lightlike submanifolds M of semi-Riemannian manifolds $widetilde{M}$ of quasi-constant curvatures. The main result is a characterization theorem for screen homothetic Einstein half lightlike submanifolds of a Lorentzian manifold of quasi-constant curvature subject to the conditions; (1) the curvature vector field of $widetilde{M}$ is tangent to M, and (2) the co-screen distribution is a conformal Killing one.