We review the parameter regions allowed by measurements of R(D(*)) and by a theoretical limit on B(Bc→τν) in terms of generic scalar and pseudoscalar new physics couplings, gs and gp. We then use these regions as constraints to predict the ranges for additional observables in b→cτν including the differential decay distributions dΓ/dq2; the ratios R(J/ψ) and R(Λc); and the tau-lepton polarization in B→D(⋆)τν, with emphasis on the CP-violating normal polarization. Finally we map the allowed regions in gs and gp into the parameters of four versions of the Yukawa couplings of the general type-III 2HDM model. We find that the model is still viable but could be ruled out by a confirmation of a large R(J/ψ).