What you describe in your original question certainly does sound like a national patent or national phase patent granted on the basis of the international application.
The PCT procedure consists of two main phases. It begins with the filing of an international application and ends (in the case of a favorable outcome for the applicant) with the grant of a number of national and/or
regional patents: hence the terms “international phase” and “national phase.” (The expression “national phase” is used even if the Office before which it takes place is a regional Office.) The expressions "international phase” and “national phase” are not actually used in the PCT, but they are convenient, short expressions which have
become customary and are therefore used in this Guide. (p. 17 of 124)
http://www.wipo.int/pct/guide/en/gdvol1/pdf/gdvol1.pdf
However, I can't see how Teilpatent can be translated as anything other than divisional patent. Could you perhaps post some examples of its use in the original German?
The translation workplace 
peer agreement (net): +2
