Context : In the Solar System , minor bodies and dust deliver various materials to planetary surfaces .
Several exoplanetary systems are known to host inner and outer belts , analogues of the main asteroid belt and the Kuiper belt , respectively .

Aims : We study the possibility that exominor bodies and exodust deliver volatiles and refractories to the exoplanets in the well-characterised system HR 8799 .

Methods : We performed N-body simulations to study the impact rates of minor bodies in the system HR 8799 .
The model consists of the host star , four giant planets ( HR 8799 e , d , c , and b ) , 650,000 test particles representing the inner belt , and 1,450,000 test particles representing the outer belt .
Moreover we modelled dust populations that originate from both belts .

Results : Within a million years , the two belts evolve towards the expected dynamical structure ( also derived in other works ) , where mean-motion resonances with the planets carve the analogues of Kirkwood gaps .
We find that , after this point , the planets suffer impacts by objects from the inner and outer belt at rates that are essentially constant with time , while dust populations do not contribute significantly to the delivery process .
We convert the impact rates to volatile and refractory delivery rates using our best estimates of the total mass contained in the belts and their volatile and refractory content .
Over their lifetime , the four giant planets receive between 10 ^ { -4 } and 10 ^ { -3 } M _ { \Earth } of material from both belts .

Conclusions : The total amount of delivered volatiles and refractories , { 5 \times 10 ^ { -3 } \textrm { M } _ { \Earth } } , is small compared to the total mass of the planets , 11 \times 10 ^ { 3 } \textrm { M } _ { \Earth } .
However , if the planets were formed to be volatile-rich , their exogenous enrichment in refractory material may well be significant and observable , for example with JWST-MIRI .
If terrestrial planets exist within the snow line of the system , volatile delivery would be an important astrobiological mechanism and may be observable as atmospheric trace gases .