  Context. It has been reported that the boundary between the umbra and the
penumbra of sunspots occurs at a canonical value of the strength of the
vertical magnetic field, independently of the size of the spot. This critical
field strength is interpreted as to be the threshold for the onset of
magnetoconvection.
  Aims. Here we investigate the reasons why this criterion, also called the
Jur\v{c}\'ak criterion in the literature, does not always identify the boundary
between umbra and penumbra.
  Methods. We perform a statistical analysis of 23 sunspots observed with
Hinode/SOT. We compare the properties of the continuum intensity and the
vertical magnetic field between filaments and spines and how they vary between
spots of different sizes.
  Results. We find that the inner boundary of the penumbra is not related to a
universal value of the vertical magnetic field. The properties of spines and
filaments vary between spots of different sizes. Both components are darker in
larger spots and the spines exhibit stronger vertical magnetic field. These
variations of the properties of filaments and spines with spot size are also
the reason for the reported invariance of the averaged vertical magnetic field
at 50% of the mean continuum intensity.
  Conclusions. The formation of filaments and the onset of magnetoconvection
are not related to a canonical value of the strength of the vertical magnetic
field. Such a seemingly unique magnetic field strength is rather an effect of
the filling factor of spines and penumbral filaments.
