I was a part owner of an estate with my mom and brother. My brother
took my mom and I to court to get his land immediately. After a three
year battle, I bowed out and signed over my inheritance back to my
mom. It amounts to about 150,000. Do I owe taxes, do I report this as
giving back on my taxes?

Before you gave anything away you should have consulted with an
attorney to figure out the tax consequences.  If probate was complete
and you owned the property you did not "give the inheritance back" 
you made a gift of it to your mother.  If you
have not completed the deeding process you can get the advice now
before doing anything.  If you have you may have tax consequences.

Which country are you in?