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 <tt>{@link Ext.form.TextField#grow grow}=true</tt>
         * (defaults to <tt>60</tt>)
         */
        growMin : 60,
        /**
         * @cfg {Number} growMax The maximum height to allow when <tt>{@link Ext.form.TextField#grow grow}=true</tt>
         * (defaults to <tt>1000</tt>)
         */
        growMax: 1000,
        growAppend : '&#160;\n&#160;',

        enterIsSpecial : false,

        /**
         * @cfg {Boolean} preventScrollbars <tt>true</tt> to prevent scrollbars from appearing regardless of how much text is
         * in the field. This option is only relevant when {@link #grow} is <tt>true</tt>. Equivalent to setting overflow: hidden, defaults to
         * <tt>false</tt>.
         */
        preventScrollbars: false,
        /**
         * @cfg {String/Object} autoCreate <p>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 <tt>{@link Ext.Component#autoEl autoEl}</tt> for details.  Defaults to:</p>
         * <pre><code>{tag: "textarea", style: "width:100px;height:60px;", autocomplete: "off"}</code></pre>
         */

        // 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.removeNode(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
        doAutoSize : function(e){
            return !e.isNavKeyPress() || e.getKey() == e.ENTER;
        },

        // inherit docs
        filterValidation: function(e) {
            if(!e.isNavKeyPress() || (!this.enterIsSpecial && e.keyCode == e.ENTER)){
                this.validationTask.delay(this.validationDelay);
            }
        },

        /**
         * 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,
                v = Ext.util.Format.htmlEncode(el.dom.value),
                ts = this.textSizeEl,
                h;

            Ext.fly(ts).setWidth(this.el.getWidth());
            if(v.length < 1){
                v = "&#160;&#160;";
            }else{
                v += this.growAppend;
                if(Ext.isIE){
                    v = v.replace(/\n/g, '&#160;<br />');
                }
            }
            ts.innerHTML = v;
            h = Math.min(this.growMax, Math.max(ts.offsetHeight, this.growMin));
            if(h != this.lastHeight){
                this.lastHeight = h;
                this.el.setHeight(h);
                this.fireEvent("autosize", this, h);
            }
        }
    });
    Ext.reg('textarea', Ext.form.TextArea);