It's very simple answer ;
gmap.setMyLocationEnabled(true); ==> means "to center the map on my current location"
gmap.setMyLocationEnabled(false); ==> means "NOT to center the map on my current location"
[update]
If you want to remove your Location Button on your map, search this below in your code and delete it;
public void setMyLocationButtonEnabled(View v) {
if (!checkReady()) {
return;
}
// Enables/disables the my location button (this DOES NOT enable/disable the my location
// dot/chevron on the map). The my location button will never appear if the my location
// layer is not enabled.
mUiSettings.setMyLocationButtonEnabled(((CheckBox) v).isChecked());
}
public void setMyLocationLayerEnabled(View v) {
if (!checkReady()) {
return;
}
// Enables/disables the my location layer (i.e., the dot/chevron on the map). If enabled, it
// will also cause the my location button to show (if it is enabled); if disabled, the my
// location button will never show.
mMap.setMyLocationEnabled(((CheckBox) v).isChecked());
}