The best thing about Scrum, is that it is an amazing tool for identifying bad practices. This is one of the cases. An agile team should be working with as many hands as possible, on the same requirement (requirement, feature, user story - same thing). The division of work between members should be based on the tasks needed to complete the requirement, no the requirements themselves.
Each task would be defined based on the modifications that need to be made to a certain component. Doing that will not only make the problem go away (nobody's working on the same code), but will unite the team members' efforts, and make them function as a real team, rather than a disparate group of individuals that happen to share a room and a manager.
As for official information on the subject, I can suggest reading any book about Scrum, but you might want to focus on the following sites:
A few great books:
And finally, if you pardon the shameless plug, you can check out my blog - I have a few posts on this subject (such as this one) and others from my experience about implementing agile methods in software teams.