Thank you everyone to taking time into my question. Actually I am now planning my future education in SJD program in public international law. I have heard that if I want to study SJD in top universities in US or UK, the university which I choose for LLM will affect the opportunities (acceptance rate) to study SJD in top universities.

For example in US, if I want to study SJD in maybe Harvard or Yale Law School, I need to get admission only into LLM program in Harvard or Yale. However, LLM certificate in that top university doesnt guarantee your admission into SJD program. So do you know which university gives more rates of acceptance to get into SJD program?

My idealistic universities (if I can) are Harvard, Yale, NYU in US or Oxford, Cambridge in UK.

I think that that's pretty close to the case.

This is what Harvard's SJD page says:

We currently have over 70 S.J.D. candidates overall (some 50 in residence) representing more than 30 countries, drawn primarily from among Harvard's top LL.M. graduates.

The Doctor of the Science of Law (J.S.D.) program is a select program open only to graduates of the LL.M. program at Yale Law School

Thank you for your response. I will also try to look in each website's university.