I think each "arm" has to have some of the center to survive. Actually found this on wiki...
Some species of sea star also reproduce asexually by fragmentation, often with part of an arm becoming detached and eventually developing into an independent individual sea stars. This has led to some notoriety. Sea stars can be pests to fishermen who make their living on the capture of clams and other mollusks at sea as sea stars prey on these. The fishermen would presumably kill the sea stars by chopping them up and disposing of them at sea, ultimately leading to their increased numbers until the issue was better understood. A sea-star arm can only regenerate into a whole new organism if some of the central ring of the sea star is part of the chopped off arm.
Edit: Also found this on wiki...
Some species of sea star have the ability to regenerate lost arms and can regrow an entire new arm in time. Most species must have the central part of the body intact to be able to regenerate, but a few can grow an entire sea star from a single ray. Included in this group are the red and blue Linckia star. The regeneration of these stars is possible due to the vital organs kept in their rays.