Greetings,
To divide the responsibilities in the horizontal structure you may use the Skill/Will strategy. For vertical it needs to be a gradually escalating one. Request you to view the link to set the guideline for Purchase - Authority matrix
How to implement Purchasing Spending Authority Matrix? - Toolbox for IT Groups
For HR, there would be tasks and priorities. Please choose the one nearest to the task, while allocating authority. This would pace up the decision making. Here's a link to give you an idea of allocating responsibilities and distributing authority.
HR Maturity Matrix - Human Resources Strategy
HR Delegations of Authority Matrix
Once you have delegated authorities, you need to set a limit of how much can one leader decide at his or her level and when that gets escalated. The span and the time frame would be crucial as you need to ensure, there are no duplication and bottlenecks.
Please do write back with your queries. Let’s design this structure.
Regards,
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