I have a point feature class and a polygon feature class (NTA - Neighborhood Tabulation Areas). I want to assign each record in the point feature class an NTA that it falls into. Also, neither of these feature classes has a common field.

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A simple Intersect between the two layers will give you the NTA attributes on each of the points. This assumes you have a one polygon for each point relationship. If a point could fall in more than one polygon (unlikely given your data description), you'd need something different. Also, any points that do not fall in a polygon will be dropped. For other options and more detailed explanations, see my answer at How to determine which polygons, if any, points fall within?.

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