If a child goes to live with the other parent , who then does not claim CHB , and the first parent tells the CHB centre of the move , is CHB not paid to either parent?

Thanks.

Not necessarily. You can still claim Ch B for a child who doesn't live with you if you are supporting them at least to the extent of the amount of the benefit. But if they stop paying it to A they cannot start paying it to B without a claim from B.

Just out of interest I will tell you what has actually happened in this case. The mother reported that the child had gone to live with father from a certain date , and the CHB centre asked if the child would be keeping any personal effects at Mother's house and if he would be coming back to stay every so often , the answer to these questions was yes , and the CHB will continue to be paid to the mother , until a competing claim is received. The father seems reluctant to claim , as the child will be 18 in June and going to Uni in Oct , so he doesn't think it will be worth it.
So I judge from this that the mother will continue to receive the CHB.