My mother passed away in 1999, I was living with her at the time and am still living in her house today. I pay all the bill that are still in her name. What rights of ownership do I have?

None. Who inherited her estate and did she leave a Will?

You can be evicted by the "true" owner - if you did not inherit the property.

No, she left no will. And no other person to clame the property.