This is what I have...
... and I would like to assign the points to the polygons that they belong to. In ArcGIS this is accomplished fairly easy through using Spatial Join, but I have no clue how to do this task in MapInfo Professional v10.0.
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This is a relatively easy process to perform in MapInfo. There isn't a Spatial Join tool in MapInfo, per se. However, you can do the join using the Update Column tool. Note, I'm using 12.5, but the steps are the same in 10.0.
I created a polygon table called Polygon and gave it a field called PolyID. I also created a point table called Point and gave it a field called PointID and another called PolyID.
Polygon overlayed with Points looks like this:
Under the Table Menu, select Update Column...
You want to update your point table and the column which corresponds to the polygon ID. Get the value from the Polygon layer. You want to calculate the value of the Polygon ID. See below image of the dialog box:
Before pressing OK, click on the Join... button.
Specify the join where object from table Polygon intersects object from table Point.
To show that this worked, here's an image of the points displayed thematically by PolyID: