Whoever becomes Scotland's new first minister, the umbilical cord to Westminster will ostensibly slacken still further.

Not one of the contenders in the frame has served at Westminster. Most have never even been Westminster candidates. Their political milieu is Holyrood.

In Wales, Labour has openly recognised that the initial effort to impose Downing Street's will was a mistake, that the Welsh party should have been left free to determine its own leadership.

In Northern Ireland, for obvious reasons of history, the parties plough their own furrow.

Henry McLeish walks away from frontline politics

So are we seeing the further fragmentation of politics in the United Kingdom? Well, yes and no.

Yes, because the devolved organisations will inevitably set out their own political stalls.

No, because, certainly as far as Scotland is concerned, the tendency was always there, has frequently been misunderstood by Westminster - and can be exaggerated.

Let us look at the office of Scottish first minister - and its occupants to date.

Donald Dewar was quintessentially a Westminster man.

Westminster culture

He could scarcely be anything else, having fought so hard to get there: losing an early foothold in Aberdeen and only returning to the Commons via a tough by-election in Glasgow Anniesland.

That is not remotely to play down his commitment to Scottish self-government.

He campaigned for devolution all his days, even when it wasn't politically popular within the Labour Party.

Donald Dewar came from the Westminster tradition

He seized with alacrity upon the opportunity to lead the first devolved executive, describing it as the culmination of his political career. But, at the same time, he was inevitably imbued with Westminster culture.

The struggle to secure the Scotland Act within Cabinet and the Westminster Parliament meant he was intensely aware of the balancing act between Scottish and London politics.

His successor, Henry McLeish, was the first post-devolution first minister.

On issues like student tuition fees and especially free personal care for the elderly, he was content - indeed sometimes determined - to take a markedly different line from Labour colleagues in Westminster, even his former protector Gordon Brown.

However, he had been an MP, indeed a minister in the Scottish Office prior to devolution. It was of course a prolonged row over his former Westminster office allowances which led to his downfall.

Gordon Brown retains a Scottish power base

Within the Scottish Cabinet and Scottish Parliamentary Labour Party, Mr McLeish has a reputation as something of a loner.

He can be affable, comradely - but is not regarded as a collective operator. Team McLeish - as they were occasionally designated - largely comprised special advisers.

The new contenders for the Scottish Labour leadership - and hence the post of first minister - come from a definable generation.

They're aged round about forty, they're bright and alert, they're New Labour (at least in the slightly distilled Scottish version of that term). They are - or have been - friends as well as colleagues.

Of course, this is imprecise stuff, a question of instinct rather than analysis. It's perhaps best explained by saying that the next Labour generation grew up taking self-government as read.

Swift coronation

Yes, they argued for it internally when required. Yes, they campaigned for it externally.

But they had no doubts, few qualms. They saw that the Scottish body politic was developing substantially - and they intended to play a part.

For example, the front runner for the post of First Minister is Jack McConnell, the present Scottish education minister.

Jack McConnell is the front-runner for first minister

He had the political courage to contest Henry McLeish for the post last year when the indications were that the Westminster hierarchy would have preferred a swift coronation after the death of Donald Dewar.

Mr McConnell only lost then by eight votes in a truncated internal election, comprising MSPs and the executive of the Scottish party.

Now he is "like a greyhound out of the trap" - as one MSP put it privately - for the coming contest which will comprise a full electoral college of party members, unions and elected representatives from Holyrood, Westminster and Europe.

Diligently loyal to Mr McLeish, Mr McConnell has nevertheless quietly sustained his own team of supporters, ready should a contest come.

He has bided his time as an able and charismatic minister: self-assured, say friends; arrogant, say critics.

Labour ethos

Crucially, Mr McConnell was also a founder member of Scottish Labour Action, an influential pressure group which agitated for maximum devolution and for the Labour party to match its external policies by transferring control over Scottish policies to the Scottish membership and executive.

Those tipped as possibles to stand against him - Wendy Alexander, Angus MacKay, Jackie Baillie, Susan Deacon - are all imbued to varying degrees by this Scottish Labour ethos.

So this is a Scottish contest for the leadership of Scottish Labour in a Scottish Parliament, a race to name a candidate for the post of Scottish First Minister.

Wendy Alexander may challenge Jack McConnell

But now the caveats. The Chancellor Gordon Brown retains an intense interest in Scottish politics - which bemuses some Westminster colleagues but is easily understood by those who know his background and ambitions.

He came up the ladder of Scottish Labour before heading to Westminster, he remains a Scottish MP and he values his domestic party power base.

Who knows when he may find it useful?

Mr Brown will be influential in the choice of Labour's next Scottish leader. No buddy of Jack McConnell, he'll favour a rival, most probably Wendy Alexander.

So, the umbilical link with Westminster in the wider sense may be weakening - but the conduit from 11 Downing Street to Holyrood remains in place.

'Quasi-nationalist

Further, it is important to avoid exaggerating the separation of Scottish Labour from the wider party.

Mr McConnell's former mates in Scottish Labour Action were occasionally described as "quasi-nationalist". If I used the phrase at all, I was careful to lay stress on "quasi".

All the main contenders for this post are committed to Labour - throughout Britain as well as simply in Scotland.

I well recall the by-election in Perth, listening as an apparatchik from Millbank berated Scottish Labour over the conduct of the campaign

BBC Scotland's Brian Taylor

All the main contenders for this post are committed to devolution - and not remotely to independence.

To be blunt, there was always a Scottish body politic - long before devolution. There was a Scottish political forum, a Scottish Office, a distinct four-party Scottish political contest.

It was simply that Westminster frequently failed to recognise the fact.

I well recall the by-election in Perth, listening as an apparatchik from Millbank berated Scottish Labour over the conduct of the campaign.

Said apparatchik had paid a fleeting visit. Perth, apparently, should be classic Tory/Labour territory.

The SNP 'complicates' matters for Labour

Tony, it was suggested darkly, expected great things. The challenge - the very existence - of the Scottish National Party simply didn't register.

As one weary Scottish Labour official told me: "They just don't get it". The Nationalists, of course, won the seat.

So, yes, there is a distinct political agenda in Scotland. That agenda does not marry entirely with Westminster's - even when the same party is dominant in both arenas.

That phenomenon would obviously be amplified were there to be different parties in charge at Holyrood and Westminster.

But this is not independence, not separation, not the break-up of Britain. It's a direct - and predictable - consequence of the Scotland Act. Welcome to devolution.