In the EditPoly Modify panel, you can go to sub-level "Element", select an element (or several) and click "Detach" button. If you want to completely break an object with many different elements, and have each of them become an object, then you need a maxScript, like this one:
baseName = "element_"
i = 0
while $.faces.count > 0 do
(
$.setSelection #Face #{1}
$.selectElement()
polyOp.detachFaces $ ($.getSelection #Face) asNode:true name:(baseName + (i as string))
i += 1
)
delete $
Select an object, execute this script, and its elements will be separated in objects.
Hope this helps.