The best way in UNA to work with the "entry unit" page is to create the child of the BxBaseModProfilePageEntry class (the modules\base\profile\classes\BxBaseModProfilePageEntry .php file). In the beginning it has the detection of the current unique identification parameter.

// get profile info
    $iProfileId = bx_process_input(bx_get('profile_id'), BX_DATA_INT);
    $iContentId = 0;
    if ('mine' == bx_get('id')) {
      $o = BxDolProfile::getInstance();
      if ($o && $iContentId = $o->getContentId())
        $_GET['id'] = $_REQUEST['id'] = $iContentId;
    } else {
      $iContentId = bx_process_input(bx_get('id'), BX_DATA_INT);
    }

    if ($iProfileId)
      $this->_oProfile = BxDolProfile::getInstance($iProfileId);

    if (!$this->_oProfile && $iContentId)
      $this->_oProfile = BxDolProfile::getInstanceByContentAndType($iContentId, $this->MODULE);

    if ($this->_oProfile) {
      $this->_aProfileInfo = $this->_oProfile->getInfo();
      $this->_aContentInfo = $this->_oModule->_oDb->getContentInfoById($this->_aProfileInfo['content_id']);
    }

So then your child class may use the

$this->_aProfileInfo['content_id']

or

$this->_oProfile->id()

elements in all blocks for the "entry" page of your module.