These operators move the coordinates of one object to align to the coordinates of another object or objects. They are mainly used to adjust areas and lines to the shapes of adjacent areas or lines within the same object set or across different object sets.
Both the Attach to and the Attach to Self operators adjust coordinates within the location precision distance parameter that is set for drawings in the View - Properties - Precision dialog. If the location precision parameter is larger than the distance between objects, the objects will be adjusted by moving the coordinate locations that define the objects to the nearest coordinate location of the reference object.
The Attach to operator attaches objects in one object set to objects in a different object set. The Attach to Self operator adjusts objects within the same object set to each other.
Example
Consider a map that shows two drawings.

One drawing, called Lines, contains a line while the other drawing, called Areas contains an area. The location precision has been set to less than the distance between the line and the area.

If we run the transform toolbar using [All objects in Lines] Attach to [All objects in Areas] then the line in Lines will be altered to become adjacent to the area in Areas.
The Attach to operator works with all types of objects. For example, areas may be attached to other areas.

Suppose we have a drawing called Gray with an area and another drawing called Yellow with another area.

If we used [All objects in Gray] Attach to [All objects in Yellow] the gray area would be adjusted to become adjacent to the yellow area.
Example
The Attach to transform will also move coordinates in parts of objects that are not near the target if the location precision distance is great enough.

Consider a drawing with three area objects, colored differently using thematic formatting to specify a different color for each area.

We will select the upper two objects and create a saved selection called Green.

We select the lower object and create a saved selection called Blue.

We run the transform toolbar with a setting of Green - Attach to - Blue and the areas in the Green saved selection will be attached to the blue object, but if the location precision distance is large enough (as it has been set for the example above) they will also be attached to each other and their other coordinates will be moved as well.
Example
Consider a drawing with three area objects, colored differently using thematic formatting to specify a different color for each area.

We will run Attach to Self using an object set of [All Objects] using three different settings for location precision. In each case we will begin with the drawing above, specify the location precision distance and then run Attach to Self.

As we increase the value of location precision distance (that is, making operations less precise)...

...coordinates will be moved more aggressively because more of them fall within the location precision distance of each other.

When working with Attach to or Attach to Self the setting used for location precision will be critical, as this value must be set appropriately given the nearness of objects being attached to objects to which they are to be attached.
Although it is theoretically possible to attach objects to themselves using the Attach to operator, if this is what we have in mind we should use the Attach to Self operator which in most cases produces much better results.
See Also