Simple answer, the 1098-T goes on your return if they are your dependents. The tuition credits/deduction go with the student's dependency.
That said, the 1098-T is only an informational document. The numbers on it are not required to be entered onto anyone's tax return. However receipt of a 1098-T frequently means you are either eligible for a tuition credit or deduction or possibly your student has taxable scholarship income. If the student needs to report scholarship income, the 1098-T may need to go on his return. Sometimes the 1098-T goes both places with the appropriate adjustments to the amounts.