IANAL, but I deal with these kinds of agreements all the time in my publishing business. Everything I say here applies only to US copyright.
Here's sample contract http://businessofillustration.com/go-illustration-contract/
See this previous question: How does copyright apply to illustrations and cover art?
First of all, everything is negotiable. You could easily hire an artist and specify that you have the right to use the image and likeness for the entire series. I assume that the reason this is coming up because you are afraid the original artist won't be available for future volumes? If you are worried about knockoffs, you could require that the image be used exclusively for your series.
Typically the illustrator will have copyright of the work, but grant you the right to use it as for the uses specified in the contract. Typically, unless otherwise specified, the artist will deliver the final image but not the source files (from Photoshop, Illustrator, etc). Everything is negotiable.
In copyright law there is something called "derivative work" which is a work based on another copyrighted work. (explained in this PDF) If you want to protect yourself from an illustrator who doesn't want to participate in future projects, you could require that you receive the right to make a derivative work of this artwork for future books in the series.
One thing which may confuse you is that some of the bigger projects will trademark the title and even the defining illustration. But trademarks are only for the biggest of big entertainment properties (Harry Potter, Star Trek, etc), not something you normally you need to worry about.
- You need the right to use and reproduce the image for marketing and promotion. This is important.
- You need to guarantee that the image or likeness can be used for
future volumes of the series, so you'd want terms giving you the
right to hire someone else to create artwork using likeness from the
- You need to figure out whether you should specify the terms for reproducing the image or the derivative image concept for future books now or later. If it were me, I would specify a set pricing formula for this volume and all future formulas, then give the illustrator the option to refuse to do the artwork for the next volume. (If worse comes to worse, you could always offer a higher rate to this same artist later).
- I personally would be happier letting the illustrator own his copyright (i.e., not making everything work for hire). Just to respect the artist, I would probably minimize the amount of restrictions on the artist's right to reuse the image in non-book projects. But that is my preference.
Obviously, a lawyer would help, but for smaller shoestring publishing just having a simple agreement is often enough. Having a lawyer would ensure that the original agreement is actually enforceable in your state.