Does forwarding a DNS to another server takes any resources?

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http://serverfault.com – I have a personal server on linode. I just finished a job for a customer and want to move his site to his personal server. The domain servers are pointing to Linode but his is now on something else. If instead of him changing his domain servers and setting up his own domain I only forward from linode to his IP will this be using my bandwidth (or other) resources? Is this recommendable or is it better that he actually changes the domain servers to his new server? (HowTos)