This is a growing concern amongst many business owners. Does your web design company own you? This may be possible if you've allowed them to host your web site for you and also register your domain name for your company.
Web design companies have a lot of control over their clients. I refer to this as "False Power". The sad reality is that most of their clients don't even know they are stuck in this potentially painful predicament. This power is usually exercised when a client of a web design company finds a better deal on hosting for their web site and they simply want to switch their hosting provider, or when the "client" wants to upgrade their web site for a better rate than their current web development provider is offering.