Tappet now is the HVA's. Major issue on the N52 in the facelift. If it doesnt go after a couple of seconds then walk away. The only way to fix is to replace the head with a modified one that BMW later introduced.
BMW will claim no damage will occur but I don't believe that.
Link to my thread, had my head replaced under warranty @ £3,420. Think I was the first on here to have the head replaced. Now BMW won't replace, instead they replace some of the HVA's which is very hit and miss.
http://www.z4-forum.com/forum/viewtopic.php?f=3&t=10937#p161535