  We unravel the spontaneous generation of vortex-bright-soliton structures in
binary Bose-Einstein condensates with a small mass imbalance between the
species confined in a two-dimensional harmonic trap where one of the two
species has been segmented into two parts by a potential barrier. To trigger
the dynamics the potential barrier is suddenly removed and subsequently the
segments perform a counterflow dynamics. We consider a relative phase
difference of $\pi$ between the segments, while a singly quantized vortex may
be imprinted at the center of the other species. The number of vortex
structures developed within the segmented species following the merging of its
segments is found to depend on the presence of an initial vortex on the other
species. In particular, a $\pi$ phase difference in the segmented species and a
vortex in the other species result in a single vortex-bright-soliton structure.
However, when the non-segmented species does not contain a vortex the
counterflow dynamics of the segmented species gives rise to a vortex dipole in
it accompanied by two bright solitary waves arising in the non-segmented
species. Turning to strongly mass imbalanced mixtures, with a heavier segmented
species, we find that the same overall dynamics takes place, while the
quench-induced nonlinear excitations become more robust. Inspecting the
dynamics of the angular momentum we show that it can be transferred from one
species to the other, and its transfer rate can be tuned by the strength of the
interspecies interactions and the mass of the atomic species.
