In Orthodoxy in Australia, so far as I can tell only the Russians preserve the use of eagle rugs, the elaborate entrance and public vesting of the bishop in the hierarchical liturgy.

Apparently in the Greeks, Serbs and Antiochians the bishop enters in mantiya, bestows a blessing (possibly while a deacon says the entrance prayers) and then goes and vests in the Sancturary with the other priests.

I am going by anecdotes, having never attended a hierarchical liturgy in these jurisdictions.

What are the initial rubrics for the hierarchical liturgy as followed by the non-Slavic Eastern Catholics (especially Italo Greek and Romanian, but also melkite if no one knows about those)?

From what I can tell, at least recently, the Ukrainian, Ruthenian etc Catholics seem to e doing things much like the Russian Orthodox, so not so curious about those.

I've been to both Greek and Serbian hierarchal Liturgies where the bishop just came in fully vested like some Greek Catholic hierarchs do.

Gresham's Law strikes again!

Fr. Serge

In the Melkite Church in Australia (and in the Middle East), the bishop may come into the church and be vested by the deacons and sub-deacons -- if the occasion is formal (e.g. ordination, important feast).
I have seen this also at the Antiochian Orthodox, here in Australia.

This public vesting, though, is not performed during most liturgies or prayer services.