  Inclusive cross sections for Higgs boson production in proton-proton
collisions are calculated in the formalism of unintegrated gluon distributions
(UGDF). Different UGDF from the literature are used. Although they were
constructed in order to describe the HERA deep-inelastic scattering $F_2$ data,
they lead to surprisingly different results for Higgs production. We present
both two-dimensional invariant cross section as a function of Higgs rapidity
and transverse momentum, as well as corresponding projections on rapidity or
transverse momentum. We quantify the differences between different UGD's by
applying different cuts on interrelations between transverse momentum of Higgs
and transverse momenta of both fusing gluons. We focus on large rapidity
region. The interplay of the gluon-gluon fusion and weak-boson fusion in
rapidity and transverse momentum is discussed. We find that above $p_T \sim$
50-100 GeV the weak-gauge-boson fusion dominates over gluon-gluon fusion.
