Will serialization be discretized as additional complexity?

I have a simple program to serialize a binary tree. Code:

public static <T> void serialize(TBST<T> tree, String fileName) throws FileNotFoundException, IOException {
        /*
         * using only 1 file will create a lot of confusion in coding.
         */
        try (ObjectOutputStream oosNodeData = new ObjectOutputStream(new FileOutputStream(fileName))) {
                preOrderSerialization(tree.getRoot(), oosNodeData);
        }
    }


    private static <T> void preOrderSerialization(TBSTNode<T> node, ObjectOutputStream oosNodeData) throws IOException {
        if (node == null) { 
            return;                                
        }

        oosNodeData.writeObject(node.element);

        preOrderSerialization(node.left, oosNodeData); 
        preOrderSerialization(node.right, oosNodeData);  
    }

      

        
        
        
      

    

As we can see, the program itself does not use additional space. However, it does what it says - it serializes. What is the complexity of the space? O (n) or O (1)? please ignore the stack space