The concept of trust plays an important role in the operation and public acceptance of today's computing environment. Although it is a difficult concept to formalize and handle, many efforts have been made towards a clear definition of trust and the development of systematic ways for trust management. Our central viewpoint is that trust cannot be defined, anymore, as consisting of a static set of rules that define systems properties that hold eternally due to the highly dynamic nature of today's computing systems (e.g. wireless networks, ad-hoc networks, virtual communities and digital territories etc.). Our approach is an effort to define trust in terms of properties that hold with some limiting probability as the the system grows and try to establish conditions that ensure that ??good?? properties hold almost certainly. Based on this viewpoint, in this paper we provide a new framework for defining trust through formally definable properties that hold, almost certainly, in the limit in randomly growing combinatorial structures that model ??boundless?? computing systems (e.g. ad-hoc networks), drawing on results that establish the threshold behavior of predicates written in the first and second order logic. We will also see that, interestingly, some trust models have properties that do not have limiting probabilities. This fact can be used to demonstrate that as certain trust networks grow indefinitely, their trust properties are not certain to be present