  We propose a new approach to studies on partial Steiner triple systems
consisting in determining complete graphs contained in them. We establish the
structure which complete graphs yield in a minimal PSTS that contains them. As
a by-product we introduce the notion of a binomial PSTS as a configuration with
parameters of a minimal PSTS with a complete subgraph. A representation of
binomial PSTS with at least a given number of its maximal complete subgraphs is
given in terms of systems of perspectives. Finally, we prove that for each
admissible integer there is a binomial PSTS with this number of maximal
complete subgraphs.
