Trie in C#

using System;
using System.Collections.Generic;

public class Trie
{
   public class TrieNode
   {
       public Dictionary<char, TrieNode> children;
       public bool isWord;

       public TrieNode()
       {
           children = new Dictionary<char, TrieNode>();
           isWord = false;
       }
   }

   private readonly TrieNode root;

   public Trie()
   {
       root = new TrieNode();
   }

   public void Put(string word)
   {
       TrieNode current = root;
       foreach(char child in word)
       {  
           if (!current.children.ContainsKey(child))
           {
               TrieNode tmp = new TrieNode();
               current.children.Add(child, tmp);
               
           }
           current = current.children[child];
       }
       current.isWord = true;
   }

   public bool Contains(string word)
   {
       TrieNode current = root;
       foreach(char child in word)
       {
           if (current.children.ContainsKey(child))
           {
               current = current.children[child];
           }
           else
           {
               return false;
           }
       }
       return current.isWord;
   }

   public void Remove(string word)
   {
       Remove(root, word, 0);
   }

   private bool Remove(TrieNode current, string word, int depth)
   {
       if(depth == word.Length)
       {
           current.isWord = false;
       }
       else
       {
           char child = word[depth];
           if (current.children.ContainsKey(child))
           {
               if(Remove(current.children[child], word, depth + 1) == false)
               {
                   current.children.Remove(child);
               }
           }
       }

       if(current.children.Count > 0)
       {
           return true;
       }
       return false;
   }

   public List<string> StartsWith(string prefix)
   {
       List<string> res = new List<string>();

       TrieNode current = root;
       foreach(char child in prefix)
       {
           // If exists: iterate down.
           if (current.children.ContainsKey(child))
           {
               current = current.children[child];
           }
           // Else, return empty list.
           else
           {
               return res;
           }
       }
       // Now at prefix, go down the sub-trees and return.
       StartsWith(current, prefix, res);
       return res;
   }

   private void StartsWith(TrieNode current, string prefix, List<string> words)
   {
       if (current.isWord)
       {
           words.Add(prefix);
       }

       // Iterate the keys
       foreach(char key in current.children.Keys)
       {
           StartsWith(current.children[key], prefix + key, words);
       }
   }
}