A flat head and a tape transport arrangement impart a wrap angle to the tape at the upstream corner of the head. The wrap angle, corner sharpness and tape stiffness are sufficient to cause a moving tape to form a hollow bump at the upstream corner, thereby creating a hollow into which entrained air can expand, causing a subambient pressure within and downstream of the bump. This pressure keeps the tape in contact with the head. It is created without the need for a groove or complex pressure relief slot(s). No contact pressure arises at the signal exchange site due to media wrap. The highest contact pressures are developed at a wrapped upstream corner. For a tape drive, traveling in both forward and reverse, the wrap can be at both the upstream and downstream (which is the reverse upstream) corners. Heads that are not flat can also be used, if the wrap angle relative to a main surface is sufficient and not too large. The wrapped head can also be used with rotating media, such as disks (floppy and hard) and rotating heads, such as helical wound heads for video recording. Multiple flat tape bearing surfaces can be separated by grooves and/or angles. Each flat can carry heads along one or more gap lines. Multiple adjacent narrow tracks can thus be written for extreme high track density recording
