I was just preparing an alternative to Jake's examples, showing how to move a existing map from div to div which maintains any changes to the extent.
Edit fiddle - JSFiddle
<!DOCTYPE html>
<html>
<head>
<meta http-equiv="Content-Type" content="text/html; charset=utf-8">
<!--The viewport meta tag is used to improve the presentation and behavior of the samples
on iOS devices-->
<meta name="viewport" content="initial-scale=1, maximum-scale=1,user-scalable=no">
<title>Sample Map</title>
<link rel="stylesheet" href="http://js.arcgis.com/3.15/dijit/themes/tundra/tundra.css">
<link rel="stylesheet" href="http://js.arcgis.com/3.15/esri/css/esri.css">
<style>
html, body {
height: 99%;
width: 99%;
}
#divMap{
height: 100%;
}
#leftPane {
width: 48%;
}
#header {
border: solid #C0C0C0 2px;
background-color: #C0C0C0;
}
.div1ButtonStyle {
width: 16px;
height: 16px;
}
.div2ButtonStyle {
width: 16px;
height: 16px;
}
</style>
<script src="http://js.arcgis.com/3.15/"></script>
<script>
var map;
require([
"dojo/parser", "esri/map", "dojo/on", "dojo/dom-construct", "dijit/Toolbar", "dijit/form/Button",
"dijit/layout/BorderContainer", "dijit/layout/ContentPane", "dijit/layout/AccordionContainer", "dojo/domReady!"
], function (
parser, Map, on, domConstruct
) {
parser.parse();
var map = new Map("divMap", {
center: [-80.734, 28.297],
zoom: 10,
basemap: "topo"
});
on(dojo.byId("div1Button"), "click", function () {
domConstruct.place("divMap", "rightPane");
})
on(dojo.byId("div2Button"), "click", function () {
domConstruct.place("divMap", "leftPane");
})
});
</script>
</head>
<body class="tundra">
<div id="content"
data-dojo-type="dijit/layout/BorderContainer"
data-dojo-props="design:'headline', gutters:true"
style="width: 100%; height: 100%; margin: 0;">
<div id="header"
data-dojo-type="dijit.layout.ContentPane" data-dojo-props="region:'top'">
<div id="navToolbar" data-dojo-type="dijit/Toolbar">
<div data-dojo-type="dijit/form/Button" id="div1Button" data-dojo-props="iconClass:'div1ButtonStyle'">Show Map in Right Pane</div>
<div data-dojo-type="dijit/form/Button" id="div2Button" data-dojo-props="iconClass:'div2ButtonStyle'">Show Map in Left Pane</div>
</div>
</div>
<div id="leftPane" data-dojo-type="dijit/layout/ContentPane" data-dojo-props="region:'left'">
<div id="divMap"></div>
</div>
<div id="rightPane" data-dojo-type="dijit/layout/ContentPane" data-dojo-props="region:'center'">
</div>
</div>
</body>
</html>