  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 $.
