Popover.js

var Popover = React.createClass({
  render: function() {
    // break this rendering tree
    return null;
  },

  componentDidMount: function() {
    var node = this.node = document.createElement('div');
    // append a node to render into later
    document.body.appendChild(node);
    this.renderContent();
  },

  componentWillReceiveProps: function(newProps) {
    // need to get updates from the outside world
    this.renderContent(newProps);
  },
  
  renderContent: function(props) {
    props = props || this.props;
    // reconnect the rendering tree with the children
    React.renderComponent(<div>{props.children}</div>, this.node);
  }
});

// Usage
var App = React.createClass({
  render: function() {
    return (
      <div>
        <Popover>
          Hello and stuff, I am rendered in `document.body`
        </Popover>
      </div>
    );
  }
});