Part of the delima may be in whether you are termed an "Employee" by the supervisor, or if you are a contractor, doing "work for hire". If you are an employee, the supervisor would need to pay your unemployment and other taxes.
However, if you are a "contractor", technically, from an IRS standpoint, they cannot provide you with ANY software, hardware, etc. If they do, then you are considered an Employee - costing the supervisor/ company money.
If you are a contractor, then you would need to develop your own client base as well. As a contractor, your supervisor is not required to provide you with a certain amount of work. If you bring in your own, great. If you are waiting for work from the supervisor, again, you are getting into the area of being an employee.
Do you have a written agreement with the supervisor?
We recently had both our corporate attorney and accountant go over this with us. We determined that from the company's better interests, we needed to term people "Contractors" and have agreements with them that was clear about their responsibilities and ours.