  We examine the dynamics associated with the miscibility-immiscibility
transition of trapped two-component Bose-Einstein condensates (TBECs) of dilute
atomic gases in presence of vortices. In particular, we consider TBECs of Rb
hyperfine states, and Rb-Cs mixture. There is an enhancement of the
phase-separation when the vortex is present in both condensates. In the case of
a singly charged vortex in only one of the condensates, there is enhancement
when the vortex is present in the species which occupy the edges at
phase-separation. But, suppression occurs when the vortex is in the species
which occupies the core region. To examine the role of the vortex, we quench
the inter-species interactions to propel the TBEC from miscible to immiscible
phase, and use the time dependent Gross-Pitaevskii equation to probe the
phenomenon of phase-separation. We also examine the effect of higher charged
vortex.
