"I paid for it; I own it" Maybe Not, Under Copyright Law

"Although the general rule is that the person who creates a work is the author [and owner] of that work, there is an exception to that principle: the copyright law defines a category of works called "works made for hire." If a work is "made for hire," the employer, and not the employee, is considered the author. The employer may be a firm, an organization, or an individual...

Whether or not a particular work is made for hire is determined by the relationship between the parties. This determination may be difficult, because the statutory definition of a work made for hire is complex and not always easily applied...To determine whether a work is made for hire, one must first ascertain whether the work was prepared by (1) an employee or (2) an independent contractor.

If a work is created by an employee..[within the scope of his or her employment]...generally the work would be considered a work made for hire...

If a work is created by an independent contractor (that is, someone who is not an employee under the general common law of agency), then the work...can be a work made for hire only if both of the following conditions are met: (1) it comes within one of the nine categories of works listed in part 2 of the definition and (2) there is a written agreement between the parties specifying that the work is a work made for hire."

Read more in this U.S. Copyright Office - Information Circular.