Already, the largest of these organisations are proving hugely influential as well as immensely wealthy. One only has to look, for instance, at the prominence in high places of some former employees of the management consultancy McKinsey. Among their number are Howard Davies, chairman of the Financial Services Authority; Adair Turner, head of the Confederation of British Industry; and William Hague, leader of the Conservative Party.
When it comes to the deals that oil the wheels of capitalism, it is hard to find one where Goldman Sachs, the highly successful investment bank, is not involved in some way. Meanwhile, Andersen Consulting has come out from under the shadow of the staggeringly fast-growing accounting firm Arthur Andersen to become the first port of call for many organisations - both public and private - looking for a complex information technology project to be put in place.
Lately, some of these organisations have indicated that they are looking to grow even faster by demonstrating an interest in selling off at least a part of their equity.
Many people believe such a move is behind Andersen Consulting's complex attempt to split itself from the mother ship, while Goldmans was on the verge of such a deal when the international financial crisis blew up. Only last month, the UK chiefs of the accountancy and management consultancy firm KPMG said they were considering floating a portion of their fast- growing consulting business.
But while such developments indicate that the biggest names in professional services have moved a long way from being small groups of people working behind discreet brass plaques, there is a sense in which they continue to behave as if this were still the case.
This is partly because of the partnership structure that makes significant numbers of employees owners of the business, even though day-to-day management decisions are devolved to small groups. But it is also because such people tend not to fit naturally into the corporate ethos.
Combine all this with the clear evidence that the best of these firms are growing much faster than the industrial companies they advise, and it is little wonder that some of those clients are seeking to emulate some of the attributes of the professional services firms - notably by giving individuals greater responsibility and by working in teams.
But they have little chance of catching up, simply because the firms have something they - to a large degree - do not: brain power.
As Mark Scott, a former executive with the media group WPP and author of a book on the currently hip subject of shareholder value, points out: "The dominant flow of people talent is from clients to service suppliers as professional firms hire away smart client individuals to institutionalise their relationships."
He adds - in The Intellect Industry (John Wiley & Sons, pounds 19.99) - that larger organisations which have tried to carry out such functions as advertising or corporate finance for themselves have tended to fail because "they can't do the single most important thing right: attract and retain the highest-calibre professionals".
If you doubt the extent to which this is true, go and talk to firms such as KPMG, Deloitte & Touche and Andersen Consulting about how they are increasingly looking for people with experience of particular industries as they turn their firms into collections of true experts rather than gifted generalists.
Once that sort of thing happens, it is a relatively straightforward jump to what one insider calls "the creation of a new kind of firm".
Pointing out that consultancy is ceasing to be an accurate description of what some of the largest organisations do, he adds that firms like his have become "facilitators helping large-scale organisations achieve goals that they haven't been able to achieve by themselves".
Mr Scott seems convinced that this is an unstoppable trend. He predicts that the biggest firms will become much more visible than they currently are.
And one of the ways in which this will be brought about is by the firms breaking out of their specialist sectors - such as accounting or law - into a broader provision of services.
That has certainly happened in his old sector of marketing services, where advertising agencies have bought PR consultancies and other specialist operations. But it is not so obviously true of such traditional professions as law and accountancy, where Arthur Andersen, for example, has had great difficulty recruiting a significant law firm to its stable.
Be that as it may, consolidation in the professional services firms will doubtless continue, and those that emerge at the top of the heap will continue to attract the best and the brightest.
This is simply because they offer the opportunity to do interesting and well-paid work in a sector that is seeing the sort of growth most others can only dream about.