  We investigate the projected minimum constraints set by next-generation
gravitational wave detectors Einstein Telescope and LISA on the abundance of
primordial black holes relative to dark matter for extended primordial black
hole mass distributions. We consider broad power law distributions for a range
of negative and positive exponents $\gamma$ and use the IMRPhenomXAS waveforms
to simulate binary sources up to mass ratios $q = 1000$ and redshifts $z=300$.
Our results show that power law mass distributions loosen the $f_\mathrm{PBH}$
constraint for increasing power law exponents, suggesting that extended
distributions do not help in evading existing constraints. Interestingly, very
negative values of $\gamma$ yield constraints close to ones derived from a
monochromatic distribution.
