Transform.TransformPoint Query

Greetings,
I've got a script which run a single line in Update(), that looks at a target object continuously:

Code (CSharp):

1. transform.LookAt(thisisthequestarrowtarget.transform);

this seems to work fine, except when I have an object with transform.position which is ultimately written in the Inspector as: 0,0,0 .... I understand this to be a position in local space, since this is a child object's position. However, the line of code above seems to understand 0,0,0 as world space, and points in the completely wrong direction.

I thought I might use: transform.transformpoint to convert the 0,0,0 from local space to it's position in world space, (and accomplish the same thing as above) with this line of code:

Code (CSharp):

1. transform.LookAt(transform.TransformPoint(thisisthequestarrowtarget.transform.position));

This compiles with no errors, but results in the arrow (pointing at it's target) spinning wildly and eventually coming into a tight spin around "some" point in outer space...

What am I doing wrong? Any thoughts?
Thanks!