The article explores the relation of the subject of a participial adverbial clause, whether expressed or implied, to the elements of the matrix clause, i.e. the degree of attachment of the participial clause. Three types of subjectless participial clauses can be distinguished using this criterion: 1. related clauses, whose subject is controlled by the matrix clause subject: 2. adjuncts whose subject controller may be recovered from the matrix clause, the sentence, or the immediate context; 3. clauses where further search for the subject controller is precluded either due to the fact that the adverbial clause is not closely integrated with the rest of the sentence (i.e. participial disjuncts, subjuncts and (near-) conjuncts), or due to its recategorization into a conjunction or preposition. In participial clauses with an overt subject a gradient of attachment to the matrix clause may be found, ranging from full corefence between a matrix clause element and the subject of the absolute down to complete absence of coreference. There appears to exist a close link between attachment and syntactic integration of the dependent clause into the sentence. An increasing degree of interpretive independence (i.e. the presence of a subordinator introducing the nonfinite clause, and an overt subject in the participial clause) is paralleled by the loosening of semantic ties between the elements of the two clauses. On the other hand, semantic ties (subject control) may compensate for the absence of syntactic ties (a subordinator). Our findings thus weaken the traditionally accepted "attachment rules" in limiting their force to subjectless participial adjuncts, where full subject control is preferred but the acceptahility of an unattached participial adjunct increases with the presence of a subordinator.