A question about null routing - would the upstream provider or the datacenter do that? Wouldn't one have to be dropping the packets at the upstream level in or

A question about null routing - would the upstream provider or the datacenter do that? Wouldn't one have to be dropping the packets at the upstream level in order to keep the pipe clear? At larger scales, is it common for the datacenter to own/control a router upstream, or would that be something that they would have to get in touch with their upstream provider to make happen?