I have a kubectl installed on the my local system. I connect to K8S running on GCP. Where does my k8s master server run ? On my local machine or on GCP?
In GCP. If you mean GKE specifically, it is running on special magic internal GKE systems you can't see directly.
It runs on GCP in a bunch of VMs managed by Google. Kubectl is a client tool using which you connect to the cluster from your local system. Kubectl uses a config file which has the address of the remote kubernetes master.