I am on the deed only, but 2 of us on the mortgage . If I give the house back to the bank, is my half satisfied on the shortfall of the mortgage e.g. $230k left on mortgage.. my house sells for $120K shortfall $90k am I still responsible for that amount?

Yes, you are. And normally you are not only responsible for "your half"; you are responsible for all of it.

I believe your calculations are off. If the amount owed is $230 K, and if the bank were to agree a short sale for $120 K, the amount you still would owe would be $110 K.

I know the responsibility is on both of us , but what happens if the other person pays nothing, but I have given the house back that is solely mine, does that mean they have to pay nothing?

If you have given a deed in lieu of foreclosure, yes. From what you have indicated, the other former owner is not obligated to pay you anything because that person did not share title ("on the deed") with you. But there may be details which you have not fully expressed. If so, see an attorney about possible legal action against the other former owner.