There are no native events to hook into for this. You need to set a timer and poll this element's dimensions in your own code.
Here's the basic version. It polls every 100ms. I'm not sure how you want to check the children's height. This assumes they'll just make their wrapper taller.
var origHeight = 0;
var origWidth = 0;
var timer1;
function testSize() {
var $target = $('#target')
if(origHeight==0) {
origWidth = $target.outerWidth();
origHeight = $target.outerHeight();
}
else {
if(origWidth != $target.outerWidth() || origHeight = $target.outerHeight()) {
alert("change");
}
origWidth = $target.outerWidth();
origHeight = $target.outerHeight();
timer1= window.setTimeout(function(){ testSize() }),100)
}
}