The maximum number of vortex lines at a given angular velocity Omega i
s obtained during deceleration when vortices annihilate at the wall of
the container. The width of the vortex-free region in the decelerated
state has been measured by cw NMR, for vortex lines with singular End
continuous core structures. It corresponds to tile limit of stability
of peripheral vortices for single and double quantization respectivel
y.