Bank of Scotland should also be unpicked from Lloyds Banking Group and Clydesdale Bank taken out of the National Australia Bank group to serve Scottish customers, Options For Scotland (OFS) said.
OFS, led by former SNP leader Gordon Wilson, dismissed unionist "scaremongering" that Scotland's banking sector is too big for a small independent country, pointing out most of its major banks are controlled from London.
This should change in the event of independence with the Scottish arms hived off and the assets from the remainder equitably shared, the Options For Scotland report on banking concluded.
Yes Scotland, the official pro-independence campaign, described the paper as "an interesting contribution" to the debate.
Mr Wilson said: "For most of the referendum campaign, the position of the major Scottish banks has been 'scaremongered' on the basis that an independent Scotland would be unable to cope with the risks of a future banking crisis, given that the country at face value possesses a higher ratio of banking activity than rUK.
"On the contrary, the problem facing Scotland is the reverse. Most of the major banks, as will be seen, are controlled from London headquarters.
"We have too few indigenous banks and too many which have 'brass plaques' nailed to their nominal Scottish head offices.
"This report looks at the prospects of nurturing and expanding this vital industry so that it can develop and expand both domestically and globally. Scotland needs to have more vision and confidence for the future."
The report calls for the Scottish banking services of RBS and retention of a Scottish stake in the assets and liabilities of the RBS 'bad bank' run as it is on a UK basis at present.
As it is in majority UK Government control this could be done in the negotiations following independence, according to OFS.
OFS says the position is different with Lloyds Bank, owner of the Bank of Scotland, since the Government has only a minority stake. Lloyds would therefore need to be persuaded that the flotation of the Bank of Scotland would be beneficial for their business as well as for Scotland, OFS said.
The flotation of Clydesdale Bank in Scotland once it returns to financial health would give Scotland a strong competitive and indigenous banking tripod on which to build, OFS said.
Report author Ian Blackford, a former merchant banker, said: "There are no UK plans to spin off the Scottish sections of banks like RBS and Lloyds who are no longer run from Scotland.
"The legacy of the financial crisis of 2007-08 is still with us, the UK banks are constrained by the failures of the past.
"We need to create the circumstances that will lead to a competitive banking market in Scotland. Independence will give Scotland the opportunity to restructure the former Scottish banks and return to them the power to contribute more sensitively and relevantly to the priorities of reviving Scotland's economy than is the case at present.
"In my view the importance of the Scottish financial services industry needs to be recognised by any incoming Scottish government. All of Scotland's political parties need to be pressed to outline their plans for the industry post-independence. It cannot be left to the SNP Government alone."
A Yes Scotland spokeswoman said: "This is an interesting contribution to the referendum debate as Scotland considers the choice of two futures."
A Scottish Government spokeswoman said: "The Scottish Government fully recognises the key role that the financial services industry plays in the Scottish economy and is absolutely committed to supporting and working with the industry to strengthen our foothold in financial and business services.
"The financial and business services industry is one of the key sectors within the Scottish Government Economic Strategy, identified as providing an opportunity to strengthen Scotland's areas of international comparative advantage and the capacity to boost productivity.
"Healthy, properly functioning banks are essential to Scotland and our economy, and are also integral to Scottish society providing employment and essential everyday services to thousands of people across the country."