We perform a comprehensive study of the allowed range for the Tevatron tt forward-backward asymmetries in six representative new physics models: a flavour-changing Z ′ boson, a scalar isodoublet, a W ′ boson, a heavy axigluon, a colour-triplet and a colour-sextet scalar. We devote special attention to the constraints from the tt tail at LHC on the parameter space, which will be dramatic if the measurements agree with the Standard Model prediction, specially for Z ′ and W ′ bosons. We also study the predictions for the charge asymmetries at LHC and compare several proposed definitions.