  Multidimensional configurations with Minkowski external space-time and a
spherical global monopole in extra dimensions are discussed in the context of
the brane world concept. The monopole is formed with a hedgehog-like set of
scalar fields \phi^i with a symmetry-breaking potential V depending on the
magnitude \phi^2 = \phi^i \phi^i. All possible kinds of globally regular
configurations are singled out without specifying the shape of V(\phi). These
variants are governed by the maximum value \phi_m of the scalar field,
characterizing the energy scale of symmetry breaking. If \phi_m < \phi_cr
(where \phi_cr is a critical value of \phi related to the multidimensional
Planck scale), the monopole reaches infinite radii while in the ``strong field
regime'', when \phi_m\geq \phi_cr, the monopole may end with a cylinder of
finite radius or possess two regular centers. The warp factors of monopoles
with both infinite and finite radii may either exponentially grow or tend to
finite constant values far from the center. All such configurations are shown
to be able to trap test scalar matter, in striking contrast to RS2 type 5D
models. The monopole structures obtained analytically are also found
numerically for the Mexican hat potential with an additional parameter acting
as a cosmological constant.
