Which is correct projection in ArcGIS Server for EPSG:3857/900913?

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I want to publish a mapservice in ArcGIS server, which will be overlayed on Google Maps or Bing Maps. For this, the Map Service needs to be in EPSG:3857/900913.

The Google Maps projection is supposed to assume a Spherical Earth Projection. So I went to

Coordinate Systems\Projected Coordinate Systems\World (Sphere-based)

There seems to be a Mercator (sphere).prj, but it does not seem to have the proper Projection parameters.

I then went to

Coordinate Systems\Projected Coordinate Systems\World

& there are 3 WGS84 based mercator projections:



I see that in a lot of ESRI literature, they use WGS 1984 Web Mercator (Auxiliary Sphere). Is that the Google Maps Projection? What is the WGS 1984 Web Mercator.prj then?

(As a bonus question, this image is from ArcGIS desktop 10.0, but does the answer again change at ArcGIS 10.1?)



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