The off-axis emergence of vortex breakdown (VB) is revealed. The steady axisymmetric flow in a vertical sealed cylinder, which is partially filled with water and the rest is filled with air, is driven by the rotating bottom disk. The numerical simulations show that VB can emerge away from the rotation axis, interface, and walls. As the rotation intensifies, VB first develops in the water region. If the water height is less (larger) than nearly one half of the cylinder radius, VB emerges off (on) the axis. As the rotation further increases, the off-axis VB ring touches the interface and then a thin countercirculation layer develops in the air flow above the water VB domain. This two-fluid VB ring shrinks (it even disappears in a very shallow whirlpool) as the interface approaches the bottom disk.