jecasc - 2:17 pm on Nov 24, 2011 (gmt 0)
As piatkow pointed out - it depends on the country. For example where I live you automatically have the copyright on any work you create (design, text), if the work exceeds a certain threshold of originality. And the copyright itself can not be transfered - only licenses for use can be granted.
So here the question would not be "who owns the design" but only if it meets a certain threshold of originality and if there was some agreement about the usage at the time of creation - for example a court could conclude from the circumstances that an unlimited license for usage has been granted.
In other countries copyrights can be transfered and there is no threshold for originality. In some countries the transfer requires a written contract in others not. So depending on where you live, and where the client lives the answer to your question differs.