Task Management Software
With your team distributed around the globe instead of just down the hall, you need task-management or bug-tracking systems. (We use Atlassian's Jira). A good task management system shows all progress at all times. So, if a customer calls, you can check on progress even if your partners are asleep because it's the middle of the night in their time zone. This also makes each individual's responsibilities clear, so there's no confusion (and unnecessary work) because the left hand doesn't know what tasks are assigned to the right hand.
Version-Control Systems
A version-control system is more than a version-control system_it's a way of life. We're religious about code review, and we don't put code into the source control until it's been reviewed. We encourage/insist that everyone -- not just global partners -- develop in small patches that are generated by our version-control system.
The patch-a-day rule helps in tracking the ramp-up process. You can nip mistakes in the bud, and you can encourage a common coding style (see my article Coding Conventions: Make Them Agile). It's far better to provide feedback at an early stage, and on small patches, than for global partners (or any team member) to guess how to best work with you. The goal is for global partners to be equal, integrated members of the team. So, giving them feedback as soon as possible lets them learn how the team works early in the process, letting them integrate faster.
And as the project goes along, everyone can see the daily progress. The North American section of a team can see what work the global team has done overnight; the global section can see what the North American part has done overnight. This also prevents team members from stepping on each other's toes, redoing work that's already been done.