There are two. The first one is a wedding gift from the University of Copenhagen to the Tasmanian-born Princess Mary, when she married Prince Frederik. Established in 2004 and commencing 2005.
The Crown Princess Mary Scholarship is established for a five-year period and is to be awarded to students from the University of Copenhagen’s Australian partner institutions.
Two scholarships of DKK 10,000 (app. A$2,200) will be available each calendar year commencing in 2005.
Eligibility
Available to current undergraduate students who are studying in: Humanities, Social Science, Science (Chemistry, Biochemistry, Earth Science, Plant Science and Zoology) or Economics (applicants should refer to the list of available courses taught in English at the University of Copenhagen below). Applicants should demonstrate a particular interest in studying at the University of Copenhagen.
Amount
The University of Copenhagen will provide DKK 10,000 (approx A$2,200) towards living expenses. In addition, if one of the successful applicants is from the University of Tasmania, UTAS will provide a further $3,000 towards expenses including airfare. In the event that the nominated University of Tasmania student is not successful but still wishes to travel on student exchange to the University of Copenhagen, UTAS will still provide $3,000 to help meet costs.
2005 recipients
Pictured: Princess Mary (centre) with Sydney University student Pia Akerman (left) and Andrew Fleming (right) from the University of Adelaide who also received a scholarship
Source
http://www.usyd.edu.au/news/84.html?newsstoryid=599
2006 recipients
Danielle Conlan fro Univ of Tas., who will be studying at the faculty of Law and Joseph Kelly from Queensland Univ. of Technology, who will study at the Math. faculty.
Princess Mary (far left) with QUT student Joseph Kelly (second from right). Also pictured are fellow scholarship recipient Danielle Conlan and University of Copenhagen Vice Chancellor Ralf Hemmingsen.
Source of info
http://www.news.qut.edu.au/cgi-bin/WebObje...ewsEventID=8431
2007 recipients
One of the recipients -Arts PhB student Phoebe Downing
http://info.anu.edu.au/mac/Newsletters_and...scholarship.asp
The other Scholarship is Crown Princess Mary Scholarship (Danish Students on Exchange to UTAS) -established in 2006 and commencing 2007.
QUOTE
HRH Crown Princess Mary has agreed to her former University, the University of Tasmania, granting an annual scholarship to a Danish student undertaking an exchange at UTAS. It will be known as the Crown Princess Mary Scholarship. Our partner universities in Denmark will each be asked to nominate one student to receive the 2007 Crown Princess Mary Scholarship. They will be encouraged to nominate highly competent students who have shown a particular interest in studying in Tasmania
Eligibility
The student will be selected from the students who have applied to study at UTAS under our exchange agreements. The Crown Princess Mary Scholarship is open to undergraduate students in all areas of study offered at the UTAS. As the Scholarship will be presented in March each year, we hope to select a student who is going to study at the University of Tasmania in Semester 1 (the Danish Spring Semester starting mid February 2007) or for the full year.
Amount
The Scholarship will provide the student with A$3,000 (approx. DKK 12,500) towards travel or accommodation costs.
Duration
One semester or one year
Source
http://www.scholarships.utas.edu.au/scm_de...=&award=284
or Wayne Goninon had some informations, that no one else had 
