  We have considered the paraxial vector erf-Gaussian beams with field
distribution in the form of the error function that are shaped by the cone of
plane waves with a fractional step of the azimuthal phase distribution
modulated by the Gaussian envelope. We have revealed that the initial
distributions of the transverse electric and transverse magnetic fields have
the form far from standard ones but at the far diffraction field the field
distributions recover nearly the symmetric form. We have also revealed that the
half-charged vortices in one of the field components can propagates up to the
Rayleigh length without essential structural transformations but then splits
into an asymmetric net of singly charged vortices.
