I am not clear with legal terms of this case. Anyone elaborate it.

If you want an answer since this is homework... you better take time and tell us what parts you DO understand and what parts you don't and why.

You don't even tell us what country, or what state if US...
make a list of terms and use your law dictionary first.
THEN ask.

It is a famous Australia case from 2004 that deals with partnership (what is required to constitute a partnership.

There are 100's of briefs on the case online, there are 100's of essays on the case online.

If you will ask more specific question, or explain what you think, I would be glad to discuss the case.

It is well described in the book "Concise Corporation Law" by Julie Cassidy. A must if you are into the study of Corporation Law.

A big issue is how it compares to the Partnership Act of 1892

This is a common case for your country, to address many of those issues.