  We compute model-independently the production rates and transverse momentum
spectra for the $B_c$ mesons in various spin-orbital states ($n\,^1S_0$,
$n\,^3S_1$, $n\,^1P_1$, and $n\,^3P_J\,(J=0,1,2)$ ) at hadron colliders via the
direct fragmentation of the bottom antiquark and via the
Altarelli-Parisi-induced gluon fragmentation. Since all the radially and
orbitally excited states below the $BD$ flavor threshold will decay, either
electromagnetically, hadronically, or a combination of both, into the
pseudoscalar ground state $1\,^1S_0$, they all contribute significantly to the
inclusive $B_c$ meson production.
