The service allows users to watch television shows on their portable devices free of charge.
It will also include a synchronisation feature that automatically transfers prescheduled shows from a TiVo digital video recorder to the iPod or PSP as they become available.
Apple's offerings can be played on computer and the new iPod players. The digital store offers a limited number of Disney TV shows, short movies and music videos.
Apple has an advantage over TiVo, however, as its videos are not interrupted by commercials, and are delivered in much smaller files.
A half-hour TV show recorded at 'medium' quality on a TiVo takes up approximately 600Mb, while a 45-minute video purchased from the iTunes store is just 200Mb.
TiVo pioneered the category of the personal video recorder, a device that uses a hard drive to store and play back TV shows. It uses an electronic programme guide to automatically record TV shows based on the user's viewing habits.
TiVo has been available in the UK, but is currently offered only in the US. The video transfer service is scheduled to become available to TiVo subscribers with a current generation Series 2 TiVo box by the first quarter of next year.
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