Through-the-road (TTR) hybrid designs using control strategies such as an equivalent consumption minimization strategy (ECMS) or an adaptive ECMS are implemented at the supplemental torque delivering electrically powered drive axle (or axles) in a manner that follows operational parameters or computationally estimates states of the primary drivetrain and/or fuel-fed engine, but does not itself participate in control of the fuel-fed engine or primary drivetrain. BSFC-type data particular to the paired-with fuel-fed engine allows an ECMS implementation (or other similar control strategy) to adapt to efficiency curves for the particular fuel-fed engine and to improve overall efficiencies of the TTR hybrid configuration.