A guide for prospective PhD students who have received an offer of admission to the Doctoral Program of EECS school of KTH.
Note that this is a draft version, and it is your personal responsibility to eventually double check and make sure you are following the regulations. This guide is only based on the personal experience of a few of my friends and myself.
TL;DR If you are eligible for third-cycle studies, AND if you have received acceptance to a third-cycle program at the EECS school of KTH, you then need to 1) Complete the application form and wait for the decision on admission to get admitted into the program, and 2) Sign the employment agreement (contract) so that you get enrolled in the doctoral program as a KTH employee. Your official job title would then be a Doctoral Student.
In the European education system, Third-cycle studies, which you can safely assume as almost equivalent to PhD studies, follow the first-cycle and second-cycle stuides (Bachelor's and Master's). You can read more about the cycles here.