Final answer:
Positive Control Service (PCS) is the correct answer as it is the service that manages dense air traffic environments near major airports, ensuring aircraft separation and control.
Step-by-step explanation:
The service that provides separation and control of aircraft operating in the relatively dense air traffic environment surrounding major airports is known as Positive Control Service (PCS). PCS involves air traffic control (ATC) providing routing and altitude instructions to ensure safe separation between aircraft in busy airspace. This is crucial near major airports where there is a high volume of arriving and departing flights. Ground Control Intercept (GCI), Precision Radar Monitoring Service (PRMS), and Airborne Intercept (AI) Service are other services, but they have different functions that do not fit the description provided in the question.