First, forget multiple-assignees. It doesn't work in real life and JIRA sensibly does not support it. There's a single user as the assignee (it is, of course, absolutely fine to create custom fields to enable something to be associated with many users or groups, but the assignee is single)
For the single assignee, there is a simple allocation method built in. You can automatically assign to the project lead or a component lead - have a look at each project's components section to set that up.
You can also assign people with simple post-functions on transitions, but these are a bit rigid (it'll always assign to Dave, there's no rules for making decisions)
If you're willing to install add-ons, or code, you have a lot of options for assignee decisions though.
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