Answer:
If you have created the intellectual property such as the graphic design and/or code in the website and you work for yourself, then you will likely own the intellectual property in the website. However, it is standard practice for web designers to assign (give away/transfer) the intellectual property in the website design to the client once the client has made full payment.
You should make sure that you have your client terms and conditions are drafted so that you either license or assign the intellectual property depending on your preference. If you work for a website design business as an employee, the intellectual property in the design is typically owned by your employer.
