We present recent results on heavy flavour production at
Tevatron Run II for typi+cally ~ 1 fb-1 of analysed p anti-p data at
s**(1/2) = 1.96 TeV.  This includes results on single and correlated open
charm and bottom cross sections, charm pair production kinematics, J/psi,
psi(2S) and X_cj cross sections and polarisation measurements in J/psi,
psi(2S), Upsilon (1S), and Upsilon (2S).