Creole languages offer an invaluable opportunity to study the processes leading to the emergence and evolution of Language, thanks to the short – typically a few generations – and reasonably well defined time-scales involved in their emergence. Another well-known case of a very fast emergence of a Language, though referring to a much smaller population size and different ecological conditions, is that of the Nicaraguan Sign Language. What these two phenomena have in common is that in both cases what is emerging is a contact language, i.e., a language born out of the non-trivial interaction of two (or more) parent languages. This is a typical case of what is known in biology as horizontal transmission. In many well-documented cases, creoles emerged in large segregated sugarcane or rice plantations on which the slave labourers were the overwhelming majority. Lacking a common substrate language, slaves were naturally brought to shift to the economically and politically dominant European language (often referred to as the lexifier) to bootstrap an effective communication system among themselves. Here, we focus on the emergence of creole languages originated in the contacts of European colonists and slaves during the 17th and 18th centuries in exogenous plantation colonies of especially the Atlantic and Indian Ocean, where detailed census data are available. Those for several States of USA can be found at http://www.census.gov/history, while for Central America and the Caribbean can be found at http://www.jamaicanfamilysearch.com/Samples/1790al11.htm. Without entering in the details of the creole formation at a fine-grained linguistic level, we aim at uncovering some of the general mechanisms that determine the emergence of contact languages, and that successfully apply to the case of creole formation.