Most reports of very long carbon nanotubes tend to be actually bundles of multiwalled tubes rather than singe ones. A paper in Nature titled Ultralong single-wall carbon nanotubes reports on the new record for a single walled tube of 4cm.
Characterisation is still an issue, as the European NanoBusiness Association will be discussing in a free workshop in Vienna next month. As one of the papers’ authors told the LA Monitor, growing the filament took about an hour, photographing it (using a mosaic of 230 pictures) took 10 hours