Extension interface patterns

public interface IHaveChildren {
    string ParentType { get; }
    int ParentId { get; }

    List<IChild> GetChildren()
}

public interface IHaveChildren {
    string ParentType { get; }
    int ParentId { get; }
}

public static class HaveChildrenExtension {
    public static List<IChild> GetChildren( this IHaveChildren ) {
        //logic to get children by parent type and id
        //shared for all classes implementing IHaveChildren
    }
}

public interface INode {
  INode Root { get; }
  List<INode> GetChildren( );
}

public interface IChildNode : INode {
  INode Parent { get; }
}

public static class NodeExtensions {
  public INode GetParent( this INode node ) {
    // If the node implements the new interface, call it directly.
    var childNode = node as IChildNode;
    if( !object.ReferenceEquals( childNode, null ) )
      return childNode.Parent;

    // Otherwise, fall back on a default implementation.
    return FindParent( node, node.Root );
  }
}

public interface ILongMethod {
  public bool LongMethod( string s, double d, int i, object o, ... );
}

...
public static LongMethodExtensions {
  public bool LongMethod( this ILongMethod lm, string s, double d ) {
    lm.LongMethod( s, d, 0, null );
  }
  ...
}

IInterface variable = new ImplementingClass();

public interface IHaveChildren
{
    string ParentType { get; }
    int ParentId { get; }
}

public interface IChildIterator
{
    IEnumerable<IChild> GetChildren();
}

public void DefaultChildIterator : IChildIterator
{
    private readonly IHaveChildren _parent;

    public DefaultChildIterator(IHaveChildren parent)
    {
        _parent = parent;
    }

    public IEnumerable<IChild> GetChildren()
    {
        // default child iterator impl
    }
}

public class Node : IHaveChildren, IChildIterator
{
    // *snip*

    public IEnumerable<IChild> GetChildren()
    {
        return new DefaultChildIterator(this).GetChildren();
    }
}

((IFirst)this).AmbigousMethod()

namespace Model
{
    class Person
    {
        public string Title { get; set; }
        public string FirstName { get; set; }
        public string Surname { get; set; }
    }
}

namespace View
{
    static class PersonExtensions
    {
        public static string FullName(this Model.Person p)
        {
            return p.Title + " " + p.FirstName + " " + p.Surname;
        }

        public static string FormalName(this Model.Person p)
        {
            return p.Title + " " + p.FirstName[0] + ". " + p.Surname;
        }
    }
}

public static List<long> GetIds<T>(this List<T> original){
        List<long> ret = new List<long>();
        if (original == null)
            return ret;

        try
        {
            foreach (T t in original)
            {
                IIDable idable = (IIDable)t;
                ret.Add(idable.getId());
            }
            return ret;
        }
        catch (Exception)
        {
            throw new Exception("Class calling this extension must implement IIDable interface");
        }