What determines default branch after "git clone"?

Beginning with Git 1.8.5, the server will send the actual branch name that HEAD points to, in the "symref" capability. If you have both a client and server newer than Git 1.8.5, it will update HEAD correctly.

Prior to that, the client will guess what HEAD may have pointed to by comparing the object ID that HEAD (ultimately) points to with all the object IDs of all the branches. It prefers a branch named refs/heads/master: if both HEAD and master point to the same object ID, then clone will set the default branch in the new repository to master.

Otherwise, the first branch with a matching OID (when the branches are sorted alphanumerically) will be the default branch. If no branches have matching OIDs, then HEAD will be set directly to the object ID (ie, a detached HEAD).

It is actually what HEAD points to. Use git symbolic-ref HEAD refs/heads/mybranch for setting HEAD. (source: http://feeding.cloud.geek.nz/posts/setting-default-git-branch-in-bare/ )

A bare repo has a HEAD, too. That's what you get when you clone it.

From the git clone documentation:

Clones a repository into a newly created directory, creates remote-tracking branches for each branch in the cloned repository (visible using git branch -r), and creates and checks out an initial branch that is forked from the cloned repository's currently active branch.

The bit about "currently active branch" is referring to the remote's HEAD revision.

If you want different behaviour, you can use --branch or -b:

--branch <name>
-b <name>
Instead of pointing the newly created HEAD to the branch pointed to by the cloned repository’s HEAD, point to <name> branch instead. In a non-bare repository, this is the branch that will be checked out. --branch can also take tags and detaches the HEAD at that commit in the resulting repository.