Also, an ebook exists in order to be read. A signed physical copy of a book exists to be put on display, so a signed ebook doesn't really fit with the purpose of a signed book. I don't display my ebooks; I read them.
That's why I'd much rather have a collection of signatures in an album of some kind. I could set the album to be my screen savers, or just show them off when ever I get a chance.
I did a little looking, and there are already several free autograph apps for iOS. One in particular does all that I want. BTW, there are also over 240 free paint apps for the iPad, and I bet a bunch could double as an autograph app.
A+ Signature Lite
This app will let you sign a blank screen or you can import an image from your photo album. So if you make a template for an event you can sign multiple versions of that template (1 for each fan). Or, if you're using a camera equipped iThing, you could take a picture of the fan+author and sign that. It also has a fair number of options for ink color and thickness. Plus you can add a typed message along with the signature.
This app doesn't support email, but it does support posting the signatures to Facebook. It's not the perfect solution, but it works.
You can sign with a fingertip, but if you plan to do this often then it might be worth investing in a compatible stylus. There are several nice ones out there that really feel like you're signing with a pen on paper.
Of course, iOS isn't your only option. There are any number of Android tablets out there that could be used for this, and there are several apps. but I couldn't find one that I though was worth trying. Do you have one you like?
And don't forget you could cobble together a laptop based option if you have a Wacom graphics tablet. Or, there's a growing number of tablet-convertibles out there that run Windows, and if you add a decent paint program you have more than enough to do a signature.