The BlackBerry Partners Fund rolled out its first wave of investment Wednesday, participating in rounds totaling $16.7 million for Buzzd, Digby, and WorldMate .

The fund, co-managed by Canada’s JLA Ventures and RBC Venture Partners, is betting that BlackBerry maker Research In Motion can hold its own in the growing smartphone market against inroads by Apple’s iPhone and handsets based on Google’s Android operating system. Both competing platforms let users download third-party software through “app stores,” a feature RIM plans to match in March.

The popularity of RIM’s devices has spread from corporate users to the consumer market, but the iPhone has grabbed market share. The BlackBerry Curve and Pearl models were the second and third top selling smartphones from June through August in the United States, behind the iPhone, which had almost a quarter of the market, according to sales tracker NPD. In his fourth-quarter conference call, Apple Chief Executive Steve Jobs gloated that Apple had overtaken RIM in handset sales, 6.1 million to 6.9 million.

In a bid to steal some of the iPhone’s thunder, RIM is rolling out two touch-screen models, the Storm and the Bold, ahead of the holiday season.

The first companies to get funding from the new venture fund reflect the corporate heritage and consumer aspirations of the BlackBerry platform.

Buzzd, which received $3.2 million in  a first round joined by Greycroft Partners, Monitor Ventures and Qualcomm Ventures, provides location-based information along with tools to connect to friends. Think Twitter meets AOL’s CityGuide.

Software from 8-year-old WorldMate, whose board members include former Apple CEO John Sculley, now managing partner at Rho Ventures, provides flight alerts and trip reminders in a mobile concierge service. Motorola Ventures and AMC Communications joins in the $8 million third round for WorldMate.

Austin, Texas-based Digby, which builds mobile store fronts for retailers, nailed down $5.5 million in a second round that was joined by prior investors.

Shares of RIM, which is a limited partner in the BlackBerry Partners Fund, climbed $1.16, or 2.5 percent, to $48.15 in Wednesday afternoon trading.