Research has already outlined the enormous potential of Computer Supported Collaborative Learning (CSCL) to facilitate effective learning processes in higher education. There is still need, though, to build up a validated model able to portray the relationships between the key elements to design and carry out online collaboration methodologies. The purpose of this study is to establish a global model, with the aim to understand the key factors affecting online collaborative learning and to analyze their interrelation, examining the influence of interaction, intra group emotional support and online collaborative tools in learning in CSCL. The study was conducted with 106 students in the context of 5 university degree subjects that implied working on CSCL projects. At the end of the projects, the students filled out a questionnaire and the resulting data was analyzed using the partial least squares (PLS) technique. The research model proved to have a good predictive level, fulfilling the 6 hypotheses proposed. Results reveal the relevance of interaction, considering teacher-student interaction as well as student-student interaction in groups during the collaboration process. Emotional support linked to intragroup work reveals itself as a fundamental pillar in collaborative learning. On the other hand, online collaborative tools have proved to contribute to interaction between group members and to sustain emotional support. Consequently, in order to model cognitive presence, social presence and teaching presence during CSCL it is necessary to promote a fluent and satisfactory interaction, rooted on the learning process and on emotional support as well as on effective management of the online tools facilitating collaboration. Results also suggest the convenience of further research on other types of interaction in the context of CSCL.