In a short article published in 1985, Dr. Roger Ekirch examines the role of transportation in the Scottish criminal justice system. He estimated that nearly 700 people (excluding political prisoners) were transported between 1718 and 1775.
Until 1747, heritable jurisdictions still existed in the Highlands with the power to banish criminals. Unfortunately, a handful of landlords declared their tenants criminals in attempts to evict them. Outside the highlands and everywhere after 1747, transportation was only for the most serious crimes (e.g. murder, horse-theft, kidnapping) and these cases were decided by the High Court of Justiciary based in Edinburgh.
Individuals with cases coming before the High Court could petition for banishment and indeed most of those exiled from Scotland in this period were petitioners. The catch was that these individuals had to arrange for their own passage to the Colonies and had to remain in jail until they could do so. This process was easier said than done, even for the wealthy.
Ekirch, A. Roger. “The Transportation of Scottish Criminals to America during the Eighteenth Century” The Journal of British Studies, Vol. 24, No. 3 (Jul., 1985), 366-374. Access the first page of the article here; see if you local library has a JSTOR subscription so you can read the rest of the article.