The title of your thread is "I Phone" (assume you mean iPhone), but you're asking how to transfer purchases from one computer to another. If you purchased an app, you can download it on your phone from the App Store.
If you want to transfer your iTunes library from one computer to another, copy the iTunes folder.
For transferring data from one system (Mac in your case) to another is done by firewire which connects two system (either two Macs or Mac with the PC). This process is called target disk mode, where one system becomes the external hard drive of another system. The file can be transferred through drag and drop amongst the systems.
Follow these simple steps to perform target disk mode operation.
Firstly turn off the system which you wish to make an external hard drive.
Use firewire cable to connect the systems. You can connect two Macs or a PC with a Mac.
Switch on the computer to be used as a hard drive. Go to System Preferences and click on the option target Disk Mode.
Restart the system.
After restart drive icon will appear on the system and displays the other system's volumes and hard drive.
Apple also has free telephone support for owners of iPhones. Just call the number I'll include below but make sure to request a product specialist who can walk you through it from start to finish. The front line phone answerers are not normally as well versed in everything as the specialists.
They've helped me enormously in the past for all kinds of issues.
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