What the percentage of time to allocate for project management?

I'm not sure I understand your question correctly, usually a 100% of the Project Manager's time. In case of a hybrid (let's say developer and Project Manager at the same time) then it should be as long as it takes, the Project Management function of the employee should be his/her priority. Make sure you do all your job functions as a Project Manager otherwise, the project will probably fail.

Project Management is a very serious profession and should not be taken lightly.

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I agree that project management is a very serioud profession. The percentage "overhead" of project management to a project is however largely depending on the nature of a project, e.g. how many people are working on the project, complexity, budget, etc.

If a project has one developer working full time for 3 months, it sure doesn't need a project manager also working full time to manage just one developer. In this example, the percentage overhead would be 50% of project (1 out of 2 full time resources is doing only project management).