FRANKFURT (Reuters) - Vodafone (>> Vodafone Group plc) agreed on a so-called domination agreement with Kabel Deutschland (>> Kabel Deutschland Holding AG), three months after its 7.7 billion euro ($10.5 billion) acquisition of Germany's largest cable company went through.

Vodafone will offer the remaining shareholders of Kabel Deutschland 84.53 euros for each of their shares, slightly more than the 84.50 euros it had offered in its takeover bid June.

Some activist shareholders, including Paul E. Singer, founder of U.S. hedge fund Elliott Asset Management, had increased their holdings in Kabel Deutschland, hoping to squeeze out a better offer.

Investors in two other German companies - utility Mainova and HVB Real Estate Bank - used this tactic successfully in other deals to get more for their shares earlier this year.

($1 = 0.7316 euros)

(Reporting by Harro ten Wolde; Editing by Maria Sheahan)