import flash.events.Event;

import flash.events.MouseEvent;

/*Below events allow the mouse move event only when mouse is down and stop the move event when mouse is up*/

stage.addEventListener(MouseEvent.MOUSE_DOWN,down)
function down(event:MouseEvent){
	stage.addEventListener(MouseEvent.MOUSE_MOVE,generate)
}
stage.addEventListener(MouseEvent.MOUSE_UP,up)
function up(event:MouseEvent){
	stage.removeEventListener(MouseEvent.MOUSE_MOVE,generate)
}

//****************************************************
/*Actual logic to generate childs, myDot is the instance name of the class Dot*/

/*stage.addEventListener(MouseEvent.MOUSE_MOVE,generate)*/
function generate(event:MouseEvent){
	var myDot:Dot=new Dot()
	addChild(myDot) /*Adding child to stage*/
	myDot.x=mouseX
	myDot.y=mouseY
	
/*To generate random size of the object or child	*/
	myDot.scaleX=myDot.scaleY=Math.random()+.2
/*To generate the random frame numbers	*/
	myDot.gotoAndStop(Math.round(myDot.totalFrames*Math.random())+1)
/*To generate random numbers of range equal to the size of stage	*/
	myDot.dx=Math.round(Math.random()*800)
	myDot.dy=Math.round(Math.random()*600)
	
	myDot.addEventListener(Event.ENTER_FRAME,update)
}

/*Here Function update is an ENTER_FRAME event.This function is executed every mili second*/

function update(event:Event){
	event.target.x+=(event.target.dx-event.target.x)/10
	event.target.y+=(event.target.dy-event.target.y)/10
	
/*To decrease the alpha value of the childs	*/

	if(Math.round(event.target.x)==Math.round(event.target.dx)){
		if(event.target.alpha>0){
			event.target.alpha-=0.5
		}
	}
}

Adding child to the stage using action script

script

ActionScript 3