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Inclusive cross sections for Higgs boson production in proton-protoncollisions are calculated in the formalism of unintegrated gluon distributions(UGDF). Different UGDF from the literature are used. Although they wereconstructed in order to describe the HERA deep-inelastic scattering $F_2$ data,they lead to surprisingly different results for Higgs production. We presentboth two-dimensional invariant cross section as a function of Higgs rapidityand transverse momentum, as well as corresponding projections on rapidity ortransverse momentum. We quantify the differences between different UGD's byapplying different cuts on interrelations between transverse momentum of Higgsand transverse momenta of both fusing gluons. We focus on large rapidityregion. The interplay of the gluon-gluon fusion and weak-boson fusion inrapidity 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.Comment: 32 pages, 18 figures, corrected version, restructured, misprints  removed, discussion added, new figure added, in print in EPJ

Unintegrated gluon distributions and Higgs boson productionin proton-proton collisions