Most MOSFETs have an internal diode (or behave as though they do) so current will flow form source to drain regardless of the state of the gate.

You dont need a super high-power transistor - normal car relays have a coil resistance of 85 ohms, which is about 150 mA at 12V. Id use a transistor with at least twice that current capacity as its an inductive load. Personally I would use a Darlington array IC - search for ULN2803 on Maplin.co.uk. This will probably be cheaper than building it out of discrete components as well.

Also, if youre using a MOSFET or NPN transistor, connect the source or emitter to ground and the load between the battery positive and drain/collector.