Even if you provide all the information for the history, the writer of the history will generally own copyright, unless you reach some arrangement to the contrary.
This is because the general rule is that the “author” of a work is the first owner of copyright. When a work is commissioned, the person who creates the work is the owner of the copyright but the paying client has a licence to use the work for the purpose(s) for which it was commissioned. This general rule can be altered by an agreement.
If you want to own copyright in a particular written version of your family history, you will need to persuade the writer to assign the copyright to you. An assignment must be in writing and signed by the copyright owner to be legally effective.