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* NatWest Markets growing business after decade of cuts

* Rebuilding relationships with financial institutions

* Rising up table for euro-denominated bond sales - data

* Growth of investment bank could be crucial for RBS

By Emma Rumney and Abhinav Ramnarayan

LONDON, March 14 (Reuters) - After a decade of deep cuts torein in a division that nearly bankrupted its parent, Royal Bankof Scotland's investment bank is attracting new businessonce again, according to executives and a review of industrydata.

The investment banking division, NatWest Markets, helpedpropel RBS's meteoric rise from a small Scottish lender to abehemoth with assets outstripping British GDP in 2008, almostderailing the economy when it emerged much of them were toxic.

Since then the unit has slashed its product lines from 28 tothree: interest-rate products; currencies; and financing, whichhelps corporate and institutional clients raise debt and acts asa market maker for their bonds.

The investment bank is beefing up financing, the smallest ofits three business areas, with one focus being rebuildingrelationships with financial customers like banks or insurersthat were lost when the bank yanked teams from a host ofgeographies.

It has risen to eighth place in the league tables ofeuro-denominated bond sales for financial institutions in 2018so far, according to Thomson Reuters data, up from 15th place in2016 and 2017, and 20th in 2015. By comparison, the investmentbank was in sixth place in 2008.

Growth at NatWest Markets could be crucial for RBS, whichrelies on the unit for almost a tenth of its revenue, as itlooks to restart dividends and faces a multi-billion-dollarsettlement with U.S. authorities for mis-selling mortgage-backedsecurities before the financial crisis.

Harsh Shah, who is leading the drive as head of financialinstitutions origination and solutions, told Reuters his teamhad been reopening dialogue with clients but declined to providean example of where this had been successful.

NatWest Markets' narrow, European focus diverges from therest of the industry, which tends to also offer equities andservices like M&A and have a more global reach.

This proved an advantage over the past year, as it benefitedfrom comparative volatility in sterling-denominated debt afterthe Brexit vote while the rest of the industry was strugglingwith subdued global markets.

But it is too early to predict the fortunes of theinvestment bank.

Its losses narrowed by almost 900 million pounds ($1.26billion) in 2017 to 977 million pounds, but it is stillwrestling with its past: restructuring and conduct costsaccounted for almost 70 percent of that loss.

NatWest Markets is far from being back in the big leaguebecause it is now a sliver of the size of its rivals as a resultof the cuts. Its 1.05 billion pounds in total revenue in 2017 isdwarfed by the 9.9 billion pounds at Barclays' investment bankand $15.1 billion in net operating income at HSBC'sinvestment bank.

'QUIETLY' GROWING

Once emblematic of RBS's penchant for risk taking andill-judged expansion, culminating in the bank's 45.5 billionpound bailout in 2008, NatWest Markets' streamlined ambitionsreflect its parent's drive to concentrate on key markets.

"It is starting to quietly grow market share again in themarkets we like," RBS Chief Executive Ross McEwan said at thebank's annual results presentation last month in response to aquestion from Reuters on plans for NatWest Markets.

He added that there were no "major" plans for expansion.

However NatWest Markets has made a small number ofsignificant hires in financing, including Shah, who was hired in2016, and two other senior people that were added to itsfinancial institutions team last year. Its government and publicorganisation debt team has also been expanded in recentmonths.

NatWest Markets acted as joint lead bookrunner or manager on74 debt transactions by financial institutions last year, upfrom 49 in 2016, according to information compiled by financialdata provider Dealogic and provided to Reuters by RBS.

Even throughout the cuts, NatWest Markets maintained itsrole as a "primary dealer" for governments, tasked with buyingtheir debt and selling it on to investors. It is a high-profilerole that helps banks win other lucrative business in thosecountries.

For example, after primary dealing for Greece throughout itscrisis years, in recent months NatWest Markets has beenappointed to manage bond sales by the National Bank of Greece,Eurobank Ergasias and Alpha Bank.

Shah said future growth in its financial institutionsbusiness would come from a push into dollar-denominated deals,as well as ongoing strength in euros and sterling.

"We're focused on growing market share further," he said.

($1 = 0.7168 pounds)

(Reporting by Emma Rumney and Abhinav Ramnarayan; Editing bySinead Cruise and Pravin Char)