Some astrophysical jets appear to be driven by black holes. As far as I know, a detailed understanding of how black holes produce jets is still under development, but one general possibility is that the jet can derive part of its power from the black hole's spin. This would allow the emitted power to exceed the rate at which energy (mass) is being consumed by the black hole. This ratio, output power divided by input power, is called the efficiency of the jet-production mechanism.
The numerical simulations described in this 2011 report predict an efficiency of $\approx 140$ percent when the spin parameter is $a=0.99$. The same report mentions "observations of active galactic nuclei with apparent $\eta\approx\text{few}\times 100$ per cent," where $\eta$ denotes the efficiency.
Question: Without knowing the details of the jet-production mechanism, can we deduce the maximum possible efficiency in the limiting case $a\to 1$? Can such a bound be deduced from theoretical bounds (like this one or this one) on the efficiency of Penrose-like processes?
Formulas for the output power as a function of $0<a<1$ are shown in this paper, but they are fits to numerical simulation results, and I don't know if the model used in the simulation attains the maximum efficiency that could be achieved in principle.
Related:
models for astrophysical relativistic jets from compact objects
