Shopping/todo multiuser list App for iphone/android

I was shopping with my wife and we where trying to grab things as efficiently as possible by dividing up the list and then meeting up with our set of items. The difficulty is that we have to constantly meet up and see who has what in order to make sure we don't end up with two of anything. One way to deal with this is for one person to start at the bottom of the list and the other to work from the top, but it still requires checking in (physically finding someone in a crowded store) to see who has what.

Now what if there was a list program for our phones which you could check off items and then have that check off transmitted to the other device. This way you could see which items your partner had grabbed and then grab ones which they have not. This could also be applied more generally to chores or errands or project management, anything that requires more than one person coordinate in order to accomplish the task. Basecamp is a project management service that has a todo list somewhat like this, but it is a website and not structured as a simple app. Basecamp has too many features and thus the convenience is reduced by having to set it up. Basecamp also costs a monthly fee which is non-trivial.

bonus points for a simple "claim" system where a person can claim an item or todo so that both parties aren't trying to complete the same item.

The key with this is simplicity and ease of use. It must be easy to check off and to "claim" items on the list. The transfer between devices must be relatively fast (3g should be able to hand this I hope). If the devices where being used in relatively close proximity it might be more efficient to directly connect between them with an adhoc network. Hoever functionality over the net would be ideal for expanding the applications: i.e. two delivery drivers working routes able to update/change routes based on traffic etc.

You could add change permissions and a hierarchical structure if you where tailoring this to a business type environment.

There seem to be quite a few todo list apps on the iphone store, however none of them seem to really focus on the real time coordination that I am ideating here. It may be too difficult due to lag times, but the data transmitted could be very simple an index # and a check with a verifier returned from the alternate device. I found one that syncs with other copies of itself, but I'm not sure how real time it is. Regardless I just post the ideas, don't verify them. Ideally they could sync cross platform irt so that a person with an android could work with one with an iphone.