So what happens with Sylas steals Karma ult?

he gets one empowered karma ability cast

I'm more curious about the AP scaling clause and him getting Jayce ranged form

I think his abilities just turns into Karma's and he can use one of them empowered once but beats me

I know a Rioter said that when he takes transforming champion's ults he transforms into their alt form, and can use all of their alt form abilities until he ults again. So for Nidalee, he becomes a Cougar. With that in mind, I'd assume Karma's R makes it so his next Q, W, or E becomes the Karma empowered version of those abilities.