If my parents pay my tuition, should it be them or me who claims it on their taxes?

[TurboTaxSusan]

You would claim the tuition on your return first, and then transfer to your parents.

Please see these TurboTax Canada FAQ for more info on how to transfer tuition in TurboTax: 

How do I claim my tuition fees?

How do I transfer my unused tuition credits to someone else?

How do I enter tuition transferred from my spouse/partner or child

How much of my child's or spouse's unused tuition credits can be transferred to me?