  We extend our previous analysis on inclusive heavy quarkonia hadroproduction
to the whole Upsilon(nS) (n=1,2,3) resonance family. We use a Monte Carlo
framework with the colour-octet mechanism implemented in the PYTHIA event
generator. We include in our study higher order QCD effects such as
initial-state emission of gluons and Altarelli-Parisi evolution of final-state
gluons. We extract some NRQCD colour-octet matrix elements relevant for
Upsilon(nS) (n=1,2,3) hadroproduction from CDF data at the Fermilab Tevatron.
Then we extrapolate to LHC energies to predict prompt bottomonia production
rates. Finally, we examine the prospect to probe the gluon density in protons
from heavy quarkonia inclusive hadroproduction at high transverse momentum and
its feasibility in LHC general-purpose experiments.
