Non-finite verbs, also frequently called unmarked verbs, constitute a large field for variationist studies in linguistics, for typology and furthermore for Usage-Based Grammars. However, the descriptive approaches to participles, infinitive and gerund currently end up in a representation of these forms as defective, impersonal and atemporal. Consequently, participles, infinitives and gerunds, on account of their unmarkness, are analysed and commented on in many cases outside the question of temporality (to the advantage of aspect) and outside any capacity to have their own subject. On the other hand, several analyses have brought to light a categorial process leading observers to consider the participles as belonging to the class of adjectives, the infinitives as belonging to the class of nouns, and the gerunds to the class of adverbs. Even if this presentation allows us establish that participles readily behave as adjectives and that gerunds are often employed as circumstants, such a perspective is intermediate and cannot resume what truly characterizes non-finite verbs. In this paper, we apply the question of scalarity and this one of (more or less local) relationship appearing between non-finite verbs and other discourse components. From a philological and usage-based grammatical framework, this article analyses some attested examples (collected in the recent periodic press) focusing on the way that non-finite verbs are more or less adjunct/conjunct to other words and simultaneously more or less linked to local or non-local discursive elements.