  We study the properties of Nambu monopoles and Z-vortices in the 3D lattice
SU(2) Higgs theory which represents the Standard Model at high temperature. We
show that the densities of the Nambu monopoles and the Z-vortices are O(1) in
the symmetric phase and generically small in the Higgs phase. Near to the
critical Higgs mass and in the vicinity of the phase transition the densities
are no more negligible in the broken phase. The percolation probability of the
Z-vortex lines is found as a new disorder parameter for this phase transition.
We conclude that the transition to the symmetric phase is accompanied by
Z-vortex condensation. Simulations comparing elementary and extended vortices
and monopoles at different \beta_G values, aiming to show that the density of
vortices and monopoles of fixed physical size might have a well-defined
continuum limit, gives encouraging but so far inconclusive results.
