This paper documents aspects of the development of a logic programming paradigm with implicit control, based in a compartmentalized con0ection graph theorem prover. Whilst the research has as it main goal the development of a language in which programs can be written with much less explicit control than PROLOG and its existing successors, a secondary goal is to exploit the immense parallelism inherent in the connection graph. This is what is in focus in this presentation. We focus initially on analysis of the extent of the parallelism inherent in the proof procedure. We characterize six different forms of parallelism These various forms of parallelism can be further classified into two classes: those associated with the performance of resolution steps, and those which are more concerned with unification. Unification is thus also a major topic of this report, and is identified as a major source of the cost of executing a logic program or proving a theorem. It turns out that deferring unification is the one of the best ways of dealing with it: hashing to perform it, and indexing to avoid it. Indexing and hashing, therefore, are our third topic.