Today we are experiencing a major reconsideration of the computing paradigm, as witnessed by the abundance and increasing frequency of use of terms such as \em ambient intelligence, \em ubiquitous computing, \em disappearing computer, \em grid computer, \em global computing and \em mobile ad-hoc networks. Systems that can be described with such terms are of a dynamic, with no clear physical boundary, nature and it seems that it is impossible (or, at least, difficult) to define sharply a number of important properties holding with certainty as well as holding throughout the whole lifetime of the system. % One such system property, which is important for the viability of a system, is \em trust. Our departure point is the assumption that it seems very difficult to define static system properties related to trust and expect that they hold eternally in the rapidly changing systems falling under the new computing paradigm. One should, rather, attempt 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 \em 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 ``shapeless'' 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.