On the exit out of the Gakhov set controlled by the subordination conditions

A Gakhov set $\mathcal G$ is the class of all holomorphic and locally univalent functions in the unit disk, which have no more than one root of the Gakhov equation. For the series of the well-known subclasses of univalent functions having the zero root of the Gakhov equation, an effective desription is given for the set of all trajectories of the exit out of $\mathcal G$; such an exit takes place when the parameter value corresponds to the sharp constant in the appropriate uniqueness condition of the root. It is shown that the exit out of $\mathcal G$ may occur due to the bifurcations of the two following types only: 1) the maximum at zero splits into two maxima and the saddle; 2) the non-zero semisaddle appears and then divides into the maximum and the saddle.