Non-Hermitian Orthogonal Polynomials on a Trefoil

We investigate asymptotic behavior of polynomials $Q_n(z)$ satisfying non-Hermitian orthogonality relations $$\int_\Delta s^kQ_n(s)\rho(s)ds =0, \quad k\in\{0,\ldots,n-1\},$$ where $\Delta$ is a Chebotar\"ev (minimal capacity) contour connecting three non-collinear points and $\rho(s)$ is a Jacobi-type weight including a possible power-type singularity at the Chebotar\"ev center of $\Delta$.