tml_ms_get_blog_signup_form()

function tml_ms_get_blog_signup_form( $user_name = '', $user_email = '', $blogname = '', $blog_title = '', $errors = '' ) {
    if ( ! is_wp_error( $errors ) ) {
        $errors = new WP_Error();
    }

    /** This filter is documented in wp-signup.php */
    $filtered_results = apply_filters( 'signup_blog_init', compact( 'user_name', 'user_email', 'blogname', 'blog_title', 'errors' ) );
    $user_name        = $filtered_results['user_name'];
    $user_email       = $filtered_results['user_email'];
    $blogname         = $filtered_results['blogname'];
    $blog_title       = $filtered_results['blog_title'];
    $errors           = $filtered_results['errors'];

    if ( tml_is_default_registration_type() && empty( $blogname ) ) {
        $blogname = $user_name;
    }

    $form = tml_get_form( 'blog_signup' );

    $fields = compact( 'user_name', 'user_email', 'blogname', 'blog_title' );
    foreach ( $fields as $field => $value ) {
        $field = $form->get_field( $field );
        if ( ! $field ) {
            continue;
        }

        $error = $errors->get_error_message( $field->get_name() );
        if ( $error ) {
            $field->set_error( $error );
        } elseif ( null !== $value ) {
                $field->set_value( $value );
        }
    }

    return $form->render();
}

View src/includes/ms-functions.php, line 1015 on GitHub