DVR's and High Definition TV

When a tv program is recorded in high definition, does TiVo or and of the current DVR's replay them in High Definition?

dish network has a high definition recording dvr yes playback is also high definition
DirecTV does also with a new combo unit costing $1000.
Time-Warner cable of NYC will be offering HD-Cable box with DVR as well. TIVO is supposed to have some HD-compatible hardware coming as well. It may already be available in the new Humax DVR.
RCN in NYC offers a HD/DVR cable box that replays in HD for about $10/mos.