Show on User Register page also

Yes, but users who do not have an account will first go to User Register :)

And there is no OpenID Selector.

So they will register there...

For me on the /user page I only have login block, plus OpenID Selector.

How can I put the register block on there as well and redirect /user/register to /user?

By default, Drupal has

/user for login block
and
/user/register
for register block.

Not sure how I can merge them.

Sure, here is login
http://www.reviewcritical.com/user

and here is register
http://www.reviewcritical.com/user/register

These urls for login and register are the default for a Drupal installation.

Ok thanks.

How about showing Openid Selector on Register page as well? Could we do that also?

Tried copy and pasting the OpenID form alter for register block to this module, but not quite there yet...

function openid_selector_form_alter(&$form, $form_state, $form_id) {
  $forms = array(
    'user_login_block' => 'user-login-form',
    'user_login' => 'user-login',
    'openid_user_add' => 'openid-user-add',
	'user_register' => 'user_register',
  );
  if (array_key_exists($form_id, $forms)) {
    $library_path = libraries_get_path('openid-selector');
    $module_path = drupal_get_path('module', 'openid_selector');
    $style = variable_get('openid_selector_style', '');
    if ($style != '' && file_exists($library_path . '/css/openid-' . $style . '.css')) {
      $style = '-' . $style;
    }
    drupal_add_css($library_path . '/css/openid' . $style . '.css', 'module');
    drupal_add_css($module_path . '/openid_selector.css', 'module');
    drupal_add_js($library_path . '/js/openid-jquery.js');
    $lang = 'en'; // default language
    global $language;
    if (file_exists($library_path . '/js/openid-jquery-' . $language->language . '.js')) {
        $lang = $language->language;
    }
    drupal_add_js($library_path . '/js/openid-jquery-' . $lang . '.js');
    drupal_add_js($module_path . '/openid_selector.js');
    $settings = array(
      'img_path' => $library_path . '/images/',
      'form_id' => $forms[$form_id],
    );
    drupal_add_js(array('openid_selector' => $settings), "setting");
  }

  if ($form_id == 'user_register') {
    drupal_add_css(drupal_get_path('module', 'openid') .'/openid.css', 'module');
    drupal_add_js(drupal_get_path('module', 'openid') .'/openid.js');
    if (!empty($form_state['post']['openid_identifier'])) {
      $form['name']['#required'] = FALSE;
      $form['pass']['#required'] = FALSE;
      unset($form['#submit']);
      $form['#validate'] = array('openid_login_validate');
    }

    $items = array();
    $items[] = array(
      'data' => l(t('Log in using OpenID'), '#'),
      'class' => 'openid-link',
    );
    $items[] = array(
      'data' => l(t('Cancel OpenID login'), '#'),
      'class' => 'user-link',
    );

    $form['openid_links'] = array(
      '#value' => theme('item_list', $items),
      '#weight' => 1,
    );

    $form['links']['#weight'] = 2;

    $form['openid_identifier'] = array(
      '#type' => 'textfield',
      '#title' => t('Log in using OpenID'),
      '#size' => ($form_id == 'user_login') ? 58 : 13,
      '#maxlength' => 255,
      '#weight' => -1,
      '#description' => l(t('What is OpenID?'), 'http://openid.net/', array('external' => TRUE)),
    );
    $form['openid.return_to'] = array('#type' => 'hidden', '#value' => url('openid/authenticate', array('absolute' => TRUE, 'query' => user_login_destination())));
  }
}