The phrase "a tiny portion of their" is correct and usable in written English.
It can be used when referring to a small part or amount belonging to a group or entity.
Example: "The researchers found that a tiny portion of their sample showed significant results."
Alternatives: "a small fraction of their" or "a minuscule part of their".
Britons spend only a tiny portion of their food budget on organics, and the marketing push aims to bring them into line with the Danes, who are the world's biggest consumers of organic food and drink.
People who start early can get away with saving a tiny portion of their pay and still have a decent chance at having enough money in retirement (in other words, their money won't run out before they die).
If a tiny portion of their turnover – we're calling for 0.25% of sales – was invested through a one-off levy in a local economic development fund this could sponsor a wave of social enterprises and new ventures to help dramatically transform the high street.
But the new consensus in Sweden, the United States, and elsewhere makes it harder to question the assumption that we have a right to decide who gets to live in certain rich countries and have access to a tiny portion of their spoils.
This time, large companies such as Countrywide Credit insisted as recently as this spring that subprime loans to those who couldn't really afford them were just a tiny portion of their book of business.
By trapping lizards and snipping off a tiny portion of their tails for DNA analysis, researchers found that adult desert skinks live in the same burrow with multiple generations of their children.
Though hedge funds' assets account for only a tiny portion of global capital under management, their trading amounts to a high percentage of investment banks' revenues in some areas of business, especially convertible bonds and distressed debt, for example.
Also, more traditional collectors might find it hard to accept why they should own a tiny portion of something that they cannot enjoy on their walls in real life.
If a tiny portion of the money went to the kids, their meals would have the proper nutrients and protein needed in a healthy diet.
It may be true that the "death to gays" pastors and their followers represent a tiny portion of evangelicals.
