Dom has an exclusivity contract with Tama. He has had several kits, many of which have been destroyed during performances. More recently he has famously used one of their transparent drum kits made from acrylic shells. Some of these drum sets include:

British racing green Starclassic Maple kit with chrome hardware.
Brown fade Starclassic Maple kit with chrome hardware.
Blue sparkle Starclassic Maple kit with chrome hardware (destroyed at the conclusion of the 2001 Origin of Symmetry / Dead Star/In Your World EP support tour, as seen on "Hullabaloo" DVD).
Grey kit (unknown composition) with chrome hardware (as seen on the "Top Of the Pops" live performance and recording of Origin Of Symmetry). Its fate is unknown.
Blue sparkle Starclassic Maple kit with chrome hardware (used during 2002 tour and Absolution recording). Its fate is unknown. At least one rack tom survived until 2003 as it was used at the Grouse Lodge sessions of the Absolution recordings.
Silver sparkle Starclassic maple kit with chrome hardware (as seen in music videos for Hyper Music, Feeling Good, Plug In Baby and Dead Star).
Custom chrome finished Starclassic Maple kit with black nickel hardware (as seen on the Absolution Tour DVD). At least four different instances of this kit have been acquired and subsequently destroyed by the band at the end of live shows, at the conclusion of the Earls Court 2004 performance, at the 2004 Glastonbury Festival and on two other occasions.
Crystal ice (transparent) Starclassic Mirage kit with white nickel hardware. This kit is still in use.
For recording he has used a blue DW kit.