Are the Alternate Team Abilities just a print and play thing or were they actually released in card form?

I can't find an answer to save my life.

PnP. On heroclix.com

I believe they were released in card form at some point. Then they became, more or less PnP only.

Recently they've found their way onto some characters' character cards.

As mirandir said above, yes and no. They were printed early on as "Alternate" team abilities, replacing the PAC TA, but with PnP, they've been mostly phased out. The new Legion Founder ATA was, as mentioned, printed on the cards of certain SLoSH figures. The only recent one I can think of off-hand that was printed was The Mighty & The Worthy ATAs, which were both printed on one card in the Fear Itself set.

As the others have said, ATAs are, by and large, print and play. However, a number of them have been released as physical cards and were handed out at Origins and Gen Con the past few years. I'm curious to see if that trend will continue this year,now that they are printing them on character cards.

I had a nice set of Marvel Feats printed up at Officemax for something around $15. They printed them 3x3, cut them out and laminated them. I've been meaning to get some ATAs done as well. I don't think I'll be doing a full set since I don't use very many of them. But it does turn heads when you have nice printed, laminated cards.