Yes. The amount depends a lot on what type of program you are in. There are also a lot of teaching assistantships and research associate positions that pay tuition and/or a stipend. If you are in a science field it is rare to pay for grad school. In other fields, only a handful of students will get funding.

For my MS, my first year was a fellowship-paid tuition and a stipend. Year 2 was a research assistantship (which aligned with my thesis, so 80% of my research served my own needs, and I did a few hours a week on things purely for my advisor.) that was also free tuition and a stipend.

do you mean grad school as in a masters degree in history, or MBA, or law, or MD?

Do any grad schools offer merit aid in the same way many undergrad colleges do? TIA.