Different branches of the slave trade across the Atlantic Ocean became illegal at different times. "Illegal" has two connotations in this context. Introducing slaves into a region (or removing them) in contravention of the laws of that region certainly qualifies, but so does buying or selling them in a region where it is still legal to do so–if the slave trader himself belongs to a country that has prohibited its citizens from carrying on the traffic. Thus, the Rhode Island slave traders who searched out markets outside the U.S. in the late eighteenth century–as one state after another outlawed the traffic–were probably the first illegal traders, if we set aside those merchants who smuggled African captives from the very outset of the Atlantic slave trade.
From the 1780s until the last slave ship arrived in Cuba in 1867, the illegal portion of the traffic grew steadily until it encompassed the whole of the slave trade. The precise point at which this happened is unclear, but it was probably in 1836. By then, all the major plantation areas of the Americas had prohibited arrivals from Africa, but some countries still allowed their citizens to participate in such activity. Much slave trading was in contravention of treaties rather than laws, and the sanctions entailed confiscation of property rather than fines, imprisonment, or death.
Conventionally, "illegal" slave trading has been taken to cover arrivals in the British Caribbean after May 1807, in the U.S. after January 1, 1808, in the French Americas after 1818, in the Spanish Caribbean after 1820, and in Brazil after 1830. By this definition, about 1.5 million Africans a large number of them children arrived illegally in the Americas–that is, about 15 percent of the people who remained alive at the end of the Middle Passage during the whole slave-trade era. In fact, the decade from 1836 to 1845 was actually one of the busiest, and as this suggests, the slave trade did not decline gradually, nor did slave owners decide they no longer wanted enslaved labor. Rather, some form of prohibition was essential to the trade's disappearance.