If a network has only one switch, does STP take place ? Also, if it does, do the ports of the switch become designated ?
Q: If a network has only one switch, does STP take place?
A: Yes. STP operations occur as they normally would, although no topology is discovered or built due to there being only a single switch. The switch will send BPDU's out any connected ports but connected devices that aren't switches will drop/ignore the BPDU's.
Q: Do the ports of the switch become designated?
A: Yes. All ports on the Root bridge that are connected to other devices, whether they be other switches or any other network device will become designated ports, since all ports on the Root bridge are designated ports.
Here's the output of the "sh spanning-tree" command from a single Cisco Catalyst 2950 switch with a single workstation connected to port Fa0/1:
It depends if you have configured it or not. I would enable it because you never know what the feature might bring (new switches). Also never underestimate the power of incompetence (someone taking a cable and putting both ends in the switch.).