* Existing shareholders will also cut stakes (Adds quotes from EQT chief executive, further background): STOCKHOLM/LONDON (Reuters) - Sweden’s EQT Partners confirmed plans to list in Stockholm on Monday as the private equity firm, one of Europe’s biggest, seeks to expand and lock horns with larger global competitors. EQT, which sources told Reuters last week would target a 4 billion euro ($4.5 billion) valuation, said it would issue at least 500 million euros of new shares, while existing shareholders will sell parts of their stakes in the initial public offering (IPO).