Step-by-step delinquent tenant eviction process, step-by-step removal of tenant eviction process, all completed forms are filed with the Clerk's Office. You must follow a legal process that starts with giving proper notice.You must then file an eviction lawsuit in the Hillsborough County Court. Edit, sign, and share hillsborough county eviction forms online. No need to install software, just go to DocHub, and sign up instantly and for free. You need to fill out a written Affidavit in Support form and an Order to Show Cause form to give to the court. Fill out the rest of the form. Check the boxes and write in the details about your situation. • Do not fill in the "Notice of Motion" section until the court gives you a hearing date. The expiration date on the form is the date the notice period runs out.