retrieve all children categories given a category id

I think the class Mage_Catalog_Model_Category already includes the function you are searching. It is called getChildren:

public function retrieveAllChilds($id = null, $childs = null) {
    $category = Mage::getModel('catalog/category')->load($id);
    return $category->getChildren();
}

 The function getChildren returns children IDs comma-separated, getChildrenCategoriesreturns an array of Mage_Catalog_Model_Category instances.

If you want to get the children categories recursively, you can use:

public function retrieveAllChilds($id = null, $childs = null) {
    $category = Mage::getModel('catalog/category')->load($id);
    return $category->getResource()->getChildren($category, true);
}