[Limdep Nlogit List] relevance of the IIA assumption to the multinomial logit model

[Durham, Cathy]

Is there any relevance of the IIA assumption to the multinomial logit model?
The relationship to conditional logit where the rhs are choice attributes is understandable,
but I it is not as obviouse where the rhs are an individual's characteristics given how the logit
model is set up. (I note that LIMDEP doesn't have one built in for mlogit but it does for clogit)
Is there a discussion of this in the literature that could be referred to better understand this?
I can program the test and the results with the third (infrequently chosen)alternative dropped, passes the IIA specification test, and just looking at the parameter estimates this seemed likely to occur.
However I'm wondering whether the construction of the model is what drives this and is why the IIA doesn't need to be tested in multinomial logit. Any leads would be welcome.