That's actually really interesting. I think it depends per organ. The prostate is supplied with blood by the inferior vesical artery. Basically by blocking this artery you are not completely blocking blood supply to the prostate. This is because the middle rectal artery and internal pudenal artery also give branches to the prostate. However, by cutting down all of these, the prostate won't receive blood. So it's not as if one artery only goes to one organ. They can divide into multiple ones which all supply the organ OR supply multiple organs.
Compare it to the coronary arteries: there are 2 (sinistra and dextra), only by blocking both you 100% shut down blood supply to the heart.
By the way, the pulmonary arteries do not supply the lungs with blood, just so you know.
Hope I helped.