In the original version of Trellis, the concept was used of dividing the board into sections and playing multiple connection games simultaneously. The board was a 17x17 checkered grid, the object being to win at least three out of the five games (whether of the adjoined 9x9 quadrants or the full board). Not long after it was described in June 2000 Games, I tried applying the multiple-game concept to Hex.
Although each quadrant game was identical in itself, two of them played an acute role on the full board and two of them played an obtuse role. This set up a strategic tension which was not present in the original version of Trellis. I called this new game quadrant Trellis and presented it in October 2001 Games. I've since changed the name to quadrant Hex, as it is best classified as a Hex variant. Also, the initial format was 14x14 with 7x7 quadrants --- I've changed it to 10x10 with 5x5 quadrants in order to encourage Hex enthusiasts to give it a whirl. I'd recommend the larger format for more serious games.
Here is a nice printable board for 14x14 quadrant Hex, courtesy of Cameron Browne.
Cameron has also kindly implemented quadrant Hex for Richard's!