Can a j engine simotaneously be a J and MKII?
Simple answer is NO!.
MK2 engine is the last of the kickstart enabled engines with roller camchain.
The J/GPZ is the last incarnation of the 1000/1100cc aircooled fours, has no provision for a kickstart and has a hyvo style camchain.
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The last?
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I probably should have said that they were the last incarnation of the Z/KZ family of aircooled fours.
The ZR1100 bears no mechanical relation to the earlier bikes and isn't a develpment of the Z1 engine.