I live close to the edge of the ARTCC region covering my area. There is no way I could talk on VHF to the control center at normal GA altitudes; it might be possible from airliner or bizjet cruise altitudes, but I'm not sure even in that case. How do pilots who are outside radio range talk to ARTCC?
In an ARTCC, there are multiple sectors controlling their own unique slice of airspace. Each sector will have at least one frequency. If the ARTCC has 40 sectors, it will have at least 40 individual frequencies. When the controller transmits, his/her voice is digitized and sent over data lines to a Remote Communications Air to Ground (RCAG) site (commonly called a rag site) that is located in or near the overlying sector's airspace. When pilots transmit to ATC, the process is reversed, resulting in an analog voice in the controller's headset. All ARTCC frequencies go through a rigorous analysis to ensure the frequency coverage matches the sector's lateral and vertical limits.
If all sectors in an ARTCC are open, the frequency or frequencies assigned to a sector are used only for aircraft in that sector. As traffic volume is reduced, sectors can be combined so that one controller is using two or more frequencies. Aircraft will hear the transmissions of the controller to aircraft in a different sector, but will not hear the responding transmission from the aircraft since it is on a different frequency. On the midnight shift, it is not uncommon to have 3 or more sectors combined, along with their assigned frequencies.
Although every sector will have at least one dedicated frequency, the voice switch allows assigning different frequencies to sectors that would not normally use them. Usually this is done in response to a frequency outage. There are also discrete frequencies used for military operations in special use airspace. Additionally, all sectors have access to guard frequency (121.5/243.0) to communicate with aircraft that are in distress or have lost radio contact.
ARTCCs don't have just one transmitter. Each one has multiple stations, connected to the central hub via wire, microwave links, fiber optics, etc. This is also why each center has multiple frequencies, because adjacent stations can't be on the same frequency or there will be interference, even if both stations are transmitting the exact same thing.