MEXICO CITY, Sept 14 (Reuters) - Sitios Latinoamerica, the new cell phone tower business spun off from telecommunications giant America Movil, petitioned Mexico's main stock index to list nearly 3.19 billion shares, the new firm announced on Wednesday.

The initial value of the public offer is only 1.57 million pesos ($78,681), according to company documents sent to the index, relative pocket change for Mexico's richest man Carlos Slim, the tycoon whose family controls an America Movil-anchored business empire.

The deal also offers America Movil shareholders rights to receive one share in the new firm for every 20 America Movil shares they hold, according to the documents.

Sitios Latinoamerica expects trading of its initial share offer to launch on Sept. 27.

America Movil shareholders last year approved the plan to spin off the new firm that owns some 36,000 towers spread across more than a dozen Latin American countries in South America, Central America and the Caribbean.

At the time, America Movil said it would contribute to Sitio Latinoamerica a portion of shares it owns in subsidiary companies that own towers and other associated infrastructure. ($1 = 19.9540 Mexican pesos) (Reporting by Noe Torres; editing by Diane Craft)