Something

    function initDropTarget (item, selector) {

       var trackMouseMovement;

        item.droppable ({
            accept: selector,
            tolerance: "pointer",
            over: function (e, ui) {
                // the second parameter to bind() can be accessed through the event as event.data
                var targetAndMoving = { target: item[0], moving: ui.draggable.element };

               trackMouseMovement = createTrackMouseMovement(blah, blah);

                item.bind ("mousemove", trackMouseMovement);    
                jQuery (theAvatar).bind ("mousemove", trackMouseMovement);
            },
            out: function (e, ui) {
                dropMarker.style.visibility = "hidden";
                item.unbind ("mousemove", trackMouseMovement);
                jQuery (theAvatar).unbind ("mousemove", trackMouseMovement);            
            },