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.