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Primordial Black Holes (PBHs) have recently attracted much attention as theymay explain some of the LIGO/Virgo/KAGRA observations and significantlycontribute to the dark matter in our universe. The next generation ofGravitational Wave (GW) detectors will have the unique opportunity to setstringent bounds on this putative population of objects. Focusing on theEinstein Telescope (ET), in this paper we analyse in detail the impact ofsystematics and different detector designs on our future capability ofobserving key quantities that would allow us to discover and/or constrain apopulation of PBH mergers. We also perform a population analysis, with a massand redshift distribution compatible with the current observational bounds. Ourresults indicate that ET alone can reach an exquisite level of accuracy on thekey observables considered, as well as detect up to tens of thousands of PBHbinaries per year, but for some key signatures (in particular high--redshiftsources) the cryogenic instrument optimised for low frequencies turns out to becrucial, both for the number of observations and the error on the parametersreconstruction. As far as the detector geometry is concerned, we find that anetwork consisting of two separated L--shaped interferometers of 15 (20)~km armlength, oriented at $45^{\circ}$ with respect to each other performs betterthan a single triangular shaped instrument of 10 (15)~km arm length, for allthe metrics considered.

Searching for Primordial Black Holes with the Einstein Telescope: impact of design and systematics