There are no general regulations on what is to be considered as a habilitation-equivalent achievement. Each university and specifically the respecitve faculty has its own regulations to that. Most often these regulations are part of the habilitation regulations and differ in subject specific requirements.
However a habilitation-equivalent achievement is most often similar to a habilitation thesis.
Several research papers published can be summarized as a cumulative habilitation (three to seven excellent papers depending on the research subject). The PhD thesis can not to be part of it. Research work that has been published by the applicant in a consortium can be submitted if the persons involvement has been substantial.
The aquisition of funding for an own junior research group and the publications of ones research work are equivalent to going through the process of habilitation. Having an own research group also gurantees greater scientific independence which is a significant advantage compared to young academics working on their habilitation under supervision of a faculty member.
A junior professorship or a tenure track professorship has meanwhile become an established alternative to habilitation. The focus here is on early independence in research and teaching. Junior professors are allowed to supervise doctorates, have teaching obligations and play an active role in academic administration. These professorships are temporary, are assessed and only some offer a tenure track option. Junior professorships are especially common in mathematics and the natural sciences, in law, economic sciences and social sciences as well as linguistics and cultural studies. (taken from Research in Germany)