Collocations for controversial - adj.

be, prove
become
remain

extremely, fairly, very, etc.
highly, intensely
a highly controversial subject

potentially
He addresses such potentially controversial issues as the role of women in society.

politically

Controversial is used with these nouns:
article, aspect, bill, book, decision, documentary, figure, incident, issue, legislation, matter, move, nature, penalty, plan, point, policy, production, proposal, question, remark, ruling, scheme, shake-up, subject, thesis, topic, trial