OK that aerial has to go it is absolutely awful, it should just unscrew from the base if you grab it and twist. As regards to the base if you remove the boot lining inside the boot and unbolt the hydraulic softtop pump placing it to one side you will see the actual aerial base bolted in position. It is held in with one bolt/nut which when removed will allow you to withdraw the base downwards, there is also a rubber gaiter on the inner wing but you will get the gist when you do it.
Here is a link to a UK eBay link of the grommet which with the aerial base removed can easily be fitted from above just make sure you get the right one for the narrow body wing.
http://www.ebay.co.uk/itm/BMW-Z3-ae...arts_Vehicles_CarParts_SM&hash=item5d3ce3e3f2
Here is also a UK eBay link to the original type aerial for your reference;
http://www.ebay.co.uk/itm/Bmw-Z3-An...arts_Vehicles_CarParts_SM&hash=item4d1505108b
However a lot of Z3 owners prefer to fit a shorter beesting type aerial rather than the above whip type aerial but that is down to your own preference;
http://www.ebay.co.uk/itm/Bee-Sting...arts_Vehicles_CarParts_SM&hash=item35b1ff476a
Hope that helps.