  Assuming an integrated luminosity of 500 fb$^{-1}$ and a center-of-mass
energy of 350 GeV, we examine the prospects for measuring branching fractions
of a Standard Model-like Higgs boson with a mass of 160 GeV at the future
linear \ee collider TESLA when the Higgs is produced via the Higgsstrahlung
mechanism, \ee \pfr HZ. We study in detail the precisions achievable for the
branching fractions of the Higgs into WW$^*$, ZZ$^*$ and \bb. However, the
measurement of BF(H \pfr \gaga) remains a great challence. Combined with the
expected error for the inclusive Higgsstrahlung production rate the uncertainty
for the total width of the Higgs is estimated.
