I'm a regular employee (of the UK presence; it's all EU, so I assume that makes things a bit easier). There's a German tax office that does the wage accounting to make sure that it follows all the rules.
The only difference to a standard German employee is this: While in Germany legally the employee owes the wage taxes, they're usually collected by the employer and passed on to the authorities. But the German tax authorities don't like to do that with foreign companies (basically because they can't hunt after them when they don't pay). So from a legal perspective, I pay the wage taxes myself (but the tax office takes care of that as well).
I never knew that was possible! I'd have imagined it could have been possible as a contractor, but not with this arrangement. Is there any particular benefit to being an employee in this case as opposed to a contractor?
The only difference to a standard German employee is this: While in Germany legally the employee owes the wage taxes, they're usually collected by the employer and passed on to the authorities. But the German tax authorities don't like to do that with foreign companies (basically because they can't hunt after them when they don't pay). So from a legal perspective, I pay the wage taxes myself (but the tax office takes care of that as well).