- Report of Foreign Issuer (6-K)

SECURITIES AND EXCHANGE COMMISSION

Washington, D.C. 20549

FORM 6-K

Report of Foreign Private Issuer
Pursuant to Rule 13a-16 or 15d-16 of the

Securities Exchange Act of 1934

For the month of May, 2010

Commission File Number 1-14493

VIVO PARTICIPAÇÕES S.A.

(Exact name of registrant as specified in its charter)

VIVO Holding Company

(Translation of Registrant's name into English)

Av. Roque Petroni Jr., no.1464, 6 ^th floor – part, "B"building
04707-000 - São Paulo, SP
Federative Republic of Brazil

(Address of principal executive office)

Indicate by check mark whether the registrant files or will file annual reports under cover Form 20-F or Form 40-F. Form 20-F ___X___ Form 40-F _______

Indicate by check mark whether the registrant by furnishing the information contained in this Form is also thereby furnishing the information to the Commission pursuant to Rule 12g3-2(b) under the Securities Exchange Act of 1934.

Yes _______ No ___X____

VIVO PARTICIPAÇÕES S.A.

Publicly-held Company
CNPJ 02.558.074/0001-73 NIRE 35.3.001.587.9-2

RELEVANT FACT

VIVO PARTICIPAÇÕES S.A. (“VIVO PART.”) communicates to the market that PORTUGAL TELECOM SGPS S.A.. disclosed the following Relevant Fact on May 10, 2010:

“A Portugal Telecom SGPS, SA (“PT”) informs that it received a non-requested, binding and unconditional offer from Telefónica S.A. (“Telefónica”) for the purchase of its 50% interest in the capital stock of Brasilcel, the controlling shareholder of Vivo Participações S.A. (“Vivo”), for the price of €5,700 million (“Offer”).

The Offer is valid until June 06, 2010. A meeting was held today by the Board of Directors to consider the Offer.

Vivo is a key asset for PT’s strategy and selling such stake would be to act contrarily to PT’s long term growth outlooks.

The Board of Directors refused the Offer by unanimous vote.”

São Paulo, May 11, 2010.

Roberto Oliveira de Lima
Chief Executive Officer
Vivo Participações S.A.

Cristiane Barretto Sales
Investor Relations Officer
Vivo Participações S.A.

VIVO – Investor Relations
Tel: +55 11 7420-1172
Email: ir@vivo.com.br
Information available from: www.vivo.com.br/ir

SIGNATURE

Pursuant to the requirements of the Securities Exchange Act of 1934, the registrant has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: May 14, 2010

VIVO PARTICIPAÇÕES S.A.

By:	/ S / Cristiane Barretto Sales
	Cristiane Barretto Sales Investor Relations Officer

FORWARD-LOOKING STATEMENTS

This press release may contain forward-looking statements. These statements are statements that are not historical facts, and are based on management's current view and estimates of future economic circumstances, industry conditions, company performance and financial results. The words "anticipates", "believes", "estimates", "expects", "plans" and similar expressions, as they relate to the company, are intended to identify forward-looking statements. Statements regarding the declaration or payment of dividends, the implementation of principal operating and financing strategies and capital expenditure plans, the direction of future operations and the factors or trends affecting financial condition, liquidity or results of operations are examples of forward-looking statements. Such statements reflect the current views of management and are subject to a number of risks and uncertainties. There is no guarantee that the expected events, trends or results will actually occur. The statements are based on many assumptions and factors, including general economic and market conditions, industry conditions, and operating factors. Any changes in such assumptions or factors could cause actual results to differ materially from current expectations.

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