Performing identity operation in PostGIS?

Install the PostGIS Addons and look at the ST_SplitAgg() example.

Here is a query doing an overlay between two independent tables and joining the attributes of the second layer to the first layer:

WITH geomtableA AS (
  SELECT 0 id, ST_GeomFromText('POLYGON((5 5, 5 7, 7 7, 7 5, 5 5))') geom
  UNION ALL
  SELECT 1 id, ST_GeomFromText('POLYGON((0 0, 0 2, 2 2, 2 0, 0 0), (0.2 0.5, 0.2 1.5, 0.8 1.5, 0.8 0.5, 0.2 0.5))') geom
  UNION ALL
  SELECT 2 id, ST_GeomFromText('POLYGON((2 0.5, 2 1.5, 4 1.5, 4 0.5, 2 0.5))') geom
), geomtableB AS (
  SELECT 3 id, ST_GeomFromText('POLYGON((1 0.2, 1 1, 3 1, 3 0.2, 1 0.2))') geom
  UNION ALL
  SELECT 4 id, ST_GeomFromText('POLYGON((1.5 1, 1.5 1.4, 2.5 1.4, 2.5 1, 1.5 1))') geom
), overlay AS (
  SELECT DISTINCT ON (geom) a.id, unnest(ST_SplitAgg(a.geom, b.geom, 0.00001)) geom
  FROM geomtableA a LEFT JOIN
       geomtableB b
  ON ST_Equals(a.geom, b.geom) OR
        ST_Contains(a.geom, b.geom) OR
        ST_Contains(b.geom, a.geom) OR
        ST_Overlaps(a.geom, b.geom)
  GROUP BY a.id
  ORDER BY geom, max(ST_Area(a.geom)) DESC
)
SELECT a.id aid, b.id bid, a.geom
FROM overlay a LEFT JOIN geomtableB b
ON ST_Within(ST_Centroid(a.geom), b.geom);