  We present the full next-to-leading order corrected differential
distributions $d^2\sigma/dp_T/dy$, $d\sigma/dp_T$ and $d\sigma/dy$ for the
semi-inclusive process $p + p\to H + 'X'$. Here $X$ denotes the inclusive
hadronic state and $p_T$ and $y$ are the transverse momentum and rapidity of
the Higgs-boson $H$ respectively. All QCD partonic subprocesses have been
included. The computation is carried out in the limit that the top-quark mass
$m_t \to \infty$ which is a very good approximation as long as $m_H,p_T < 200$
GeV. Our calculations reveal that the dominant subprocess is given by $g + g
\to H + 'X'$ but the reaction $g + q(\bar q) \to H + 'X'$ is not negligible.
Another feature is that the $K$-factor representing the ratio between the
next-to-leading order and leading order differential distributions is large. It
varies from 1.4 to 1.7 depending on the kinematic region and choice of parton
densities. We show that a reliable determination of the differential cross
sections requires good knowledge of the gluon density in the region where $x <
10^{-3}$. Further we study whether the differential distributions are dominated
at large transverse momentum by soft-plus-virtual gluon contributions. This is
of interest for the resummation of large corrections which occur near the
boundary of phase space. We also compare our results with those previously
reported in the literature.
