In the case of utilities such as gas and electric, competing companies simply bill you for the service they buy in bulk from those suppliers. The service is delivered over the same connection, regardless of the vendor, because of the nature of those utilities, only one network for each is practical.
For communications utilities:
Multiple traditional cable providers would actually build separate networks to deliver to your home. You would pay to connect to one network or the other.
For telephone and DSL internet, a secondary provider (CLEC) would lease the copper pair to your home from the primary provider (ILEC), and space in the switching center for the CLEC equipment, or just resell the ILEC service.
VOIP uses your existing DSL or cable internet, and your cable provider often will sell their digital phone and internet service on their coax (but they have a monopoly on those and TV services on their coax),