The source code

    /**
     * @class Ext.form.TextArea
     * @extends Ext.form.TextField
     * Multiline text field.  Can be used as a direct replacement for traditional textarea fields, plus adds
     * support for auto-sizing.
     * @constructor
     * Creates a new TextArea
     * @param {Object} config Configuration options
     * @xtype textarea
     */
    Ext.form.TextArea = Ext.extend(Ext.form.TextField,  {
        /**
         * @cfg {Number} growMin The minimum height to allow when {@link Ext.form.TextField#grow grow}=true
         * (defaults to 60)
         */
        growMin : 60,
        /**
         * @cfg {Number} growMax The maximum height to allow when {@link Ext.form.TextField#grow grow}=true
         * (defaults to 1000)
         */
        growMax: 1000,
        growAppend : ' \n ',
        growPad : Ext.isWebKit ? -6 : 0,

        enterIsSpecial : false,

        /**
         * @cfg {Boolean} preventScrollbars true to prevent scrollbars from appearing regardless of how much text is
         * in the field (equivalent to setting overflow: hidden, defaults to false)
         */
        preventScrollbars: false,
        /**
         * @cfg {String/Object} autoCreate A {@link Ext.DomHelper DomHelper} element spec, or true for a default
         * element spec. Used to create the {@link Ext.Component#getEl Element} which will encapsulate this Component.
         * See {@link Ext.Component#autoEl autoEl} for details.  Defaults to:
         * {tag: "textarea", style: "width:100px;height:60px;", autocomplete: "off"}
         */

        // private
        onRender : function(ct, position){
            if(!this.el){
                this.defaultAutoCreate = {
                    tag: "textarea",
                    style:"width:100px;height:60px;",
                    autocomplete: "off"
                };
            }
            Ext.form.TextArea.superclass.onRender.call(this, ct, position);
            if(this.grow){
                this.textSizeEl = Ext.DomHelper.append(document.body, {
                    tag: "pre", cls: "x-form-grow-sizer"
                });
                if(this.preventScrollbars){
                    this.el.setStyle("overflow", "hidden");
                }
                this.el.setHeight(this.growMin);
            }
        },

        onDestroy : function(){
            Ext.destroy(this.textSizeEl);
            Ext.form.TextArea.superclass.onDestroy.call(this);
        },

        fireKey : function(e){
            if(e.isSpecialKey() && (this.enterIsSpecial || (e.getKey() != e.ENTER || e.hasModifier()))){
                this.fireEvent("specialkey", this, e);
            }
        },

        // private
        onKeyUp : function(e){
            if(!e.isNavKeyPress() || e.getKey() == e.ENTER){
                this.autoSize();
            }
            Ext.form.TextArea.superclass.onKeyUp.call(this, e);
        },

        /**
         * Automatically grows the field to accomodate the height of the text up to the maximum field height allowed.
         * This only takes effect if grow = true, and fires the {@link #autosize} event if the height changes.
         */
        autoSize: function(){
            if(!this.grow || !this.textSizeEl){
                return;
            }
            var el = this.el;
            var v = el.dom.value;
            var ts = this.textSizeEl;
            ts.innerHTML = '';
            ts.appendChild(document.createTextNode(v));
            v = ts.innerHTML;
            Ext.fly(ts).setWidth(this.el.getWidth());
            if(v.length < 1){
                v = "  ";
            }else{
                v += this.growAppend;
                if(Ext.isIE){
                    v = v.replace(/\n/g, '
    ');
                }
            }
            ts.innerHTML = v;
            var h = Math.min(this.growMax, Math.max(ts.offsetHeight, this.growMin) + this.growPad);
            if(h != this.lastHeight){
                this.lastHeight = h;
                this.el.setHeight(h);
                this.fireEvent("autosize", this, h);
            }
        }
    });
    Ext.reg('textarea', Ext.form.TextArea);