Shigeru Miyamoto does
"Fascination" - music was written in 1904. The English lyric was written by Dick Manning in 1952. Peer Music owns the publishing which reverts back to Mr. Manning's estate in January 2011.
If you mean the series of casual Nintendo DS games, the copyright belongs to Ubisoft.
It becomes part of his/her estate and passes through probate the same way as any tangible asset.
4kids entertainment studios and a card making factory