Nuts

Again, the main exporting area is on the other side of the world from the original cultivation of the crop. Almonds are mentioned in the Bible, when given 'divine approval'. They were a prize ingredient in breads served to Egypt's pharaohs. Almonds are thought to have originated in China and Central Asia and explorers ate almonds while travelling the "Silk Road" between Asia and the Mediterranean. Almond trees flourished in the Mediterranean -- especially in Spain and Italy. The almond tree was brought to California from Spain in the mid-1700's by the Franciscan Padres. The moist, cool weather of the coastal missions, however, did not provide optimum growing conditions. They grew better inland.

 "Almond" is also the name of the edible and widely cultivated seed of this tree. Within the genus Prunus, it is classified with the peach in the subgenus Amygdalus,

Hazelnuts

The earliest finds of hazelnuts (Corylus) used for eating date back about 6-8000 yr BC and are mainly in UK, where they are also called cobnuts.  A national collection of cobnut varieties exists at Roughway Farm in Kent.  About 1 million tonnes of hazelnuts are harvested each year, with about seventy percent of the world's hazelnuts coming from Turkey. Child Labour exploitation of hazelnut pickers in Turkey oregon produces most of the US hazelnuts, while Chile is biggest Southern producer mainly exporting to US & Europe.

Cashew

Originally native to northeastern Brazil, the tree is now widely cultivated in Vietnam, Nigeria and India as major production countries.[

The cashew tree, originally cultivated in Brazil, was introduced to Mozambique and then India in the sixteenth century by the Portuguese, as a means of controlling coastal erosion. It was spread within these countries with the aid of elephants that ate the bright cashew fruit along with the attached nut. The nut was too hard to digest and was later expelled with the droppings. Later in the nineteenth century plantations were developed, when the tree spread to a number of other countries in Africa, Asia and Latin America.

Botanically speaking, cashew are not actually nuts but merely seeds. Culinary uses for cashew seeds are similar to uses for nuts, however, and the seeds are frequently referred to as nuts. 

The cashew nut can also be harvested in its tender form, when the shell has not hardened and is green in color. The shell is soft and can be cut with a knife and the kernel extracted - but wear gloves as the skin is toxic.

Main Cashew producing countries.  Most are produced by small farmers.

It is not just the production, it is also the processing...

Macadamia

Macadamia is a genus of four species of trees indigenous to Australia and constituting part of the plant family Proteaceae.[1][2] They are native to north eastern New South Wales and central and south eastern Queensland. The tree is commercially important for its fruit, the macadamia nut or simply macadamia. The name comes from Mueller who was appointed government botanist for Victoria by Governor Charles La Trobe in 1853, a post that was newly created for him. He examined its flora, especially the Alpine vegetation of Australia, which was previously unknown. \he gave the genus the name Macadamiain 1857 in honor of the Scottish-Australian chemist, medical teacher and politician John Macadam.[4] (nothing to do with Tar macadam)..

South Africa now main producer = over 1/3 of world market

So not quite 'on the other side of the world' but still a long way off.

Why is it the exporting country are never the same asa where originally cultivated?

Brazil Nuts

The Brazil nut (Bertholletia excelsa) is a South American tree in the family Lecythidaceae, and the name of the tree's commercially harvested edible seeds.

Around 20,000 tons of Brazil nuts are harvested each year, of which Bolivia accounts for about 50%, Brazil 40%, and Peru 10% (2000 estimates).[10] In 1980, annual production was around 40,000 tons per year from Brazil alone, and in 1970, Brazil harvested a reported 104,487 tons of nuts.[6] Brazil nuts for international trade can come from wild collection rather than from plantations. This has been advanced as a model for generating income from a tropical forest without destroying it. The nuts are gathered by migrant workers known as castanheiros.

So here is an unusual example of the main exporter also being the originator/ (Discuss!)

Groundnut

See peanut.