i love some of the throwings aspects of TCMs. As a decent grappler I know what to do once my opponent has been thrown.

With all the projections, pushes, sweeps and throws in traditional Chinese martial arts, what are you taught to do once your opponent is down?

Walk away?

Let him get up and throw him again?

What?

Serious question.

From what little I know, TCM will try to throw you in such a way that's difficult to break your fall or wrench a limb in the process. I also saw examples of some of my past instructors shifting their horse stance to drop their knee onto their opponent; maybe the kidney area or ankle joint for example.

dirty rat is correct.
In Shuai Jiao, one of the objectives is to throw the person in a way that he does not have an ability to defend himself from the fall. Some of those throws are really nasty.
Bagua Zhang also is hugely influenced by Shuai Jiao. That's why a lot of Bagua throws just would end the confrontation. Tim can show you.

Also, in context, there was not a lot of ground work done in TCM's. Weapons were deployed quickly and because of battlefield conditions there was a lot of folks around to "stomp" on you.

In the south, there's "dog styles" that have some ground work, but really they are nothing compared to BJJ/Judo and western wrestling (IMO).

good training,
Joe

http://www.thestudywithin.com
http://thestudywithin.blogspot.com

Most of the TCMA I am familiar with take a similar approach to the karate I learned back when... once they hit the floor stomp on them two or three times then assume they won't get back up. There are some drop your knee on their chest/back moves, but I think those traditionally went along with a pull a knife and slit their throat finish From a self-defense point of view staying standing and giving a few good stomps should be sufficient to ensure escape.