how much input from someone else can a student have in an essay without it being collusion?
Interestingly our university undergraduate guidelines definition of collusion only specifies working with another student. So I guess this would count as plagerism rather than collusion. 

I wonder however, if the rules for PhD students give a better definition of what is an isn't acceptable:


  It is acceptable for a student to receive the following support in
  writing the thesis from the supervisory team (that is additional to
  the advice and/or information outlined above, if the supervisory team
  has considered that this support is necessary:
  
  
  Where the meaning of text is not clear the student should be asked to
  re-write the text in question in order to clarify the meaning; 
  English
  language: If the meaning of text is unclear, the supervisory team can
  provide support in correcting grammar and sentence construction in
  order to ensure that the meaning of text is clear (if a student
  requires significant support with written English above what is
  considered to be correcting grammar and sentence construction, the
  supervisory team will, at the earliest opportunity, require the
  student to obtain remedial tuition support from the University’s
  English Language Teaching Centre); 
  The supervisory team cannot
  re-write text that changes the meaning of the text (ghost
  writing/ghost authorship in a thesis is unacceptable); 
  The supervisory
  team can provide guidance on the structure, content and expression of
  writing; 
  The supervisory team can proof-read the text. 
  6 . Anyone else who
  may be employed or engaged to proof read the text is only permitted to
  change spelling and grammar and must not be able to change the content
  of the thesis.
  


In practice, the line between proofreading (which is generally considered allowable) and plagiarism (which is not), is  fuzzy and hard to define. 

If you don't know how to prove this is happening, how do you know that it is? Someone's written work being better than their oral work would suggest is not proof, and having a father in the same field is not a crime.