Why was Tessa written out of the Highlander tv series?  Did she jump
or was she pushed?  Please provide a website link, if possible.

Alexandra Vandernoot, who played Tessa, asked to leave the show. 

"[Alexandra Vandernoot] said she wasn?t surprised at how Tessa was
written out, as she?d told them that she didn't want to go on and the
writers had two months to work out how to make a clear end to Tessa."

Homepage of Paul Edmonds: Alexandra Vandernoot, Part 1 
http://www.pedmonds.force9.co.uk/conventions/w359-2.html

"Alexandra Vandernoot (Tessa) wanted off the show..."

TiVo Community: Highlander question
http://archive.tivocommunity.com/tivo-vb/history/topic/115854-1.html

"Alexandra Vandernoot left the series because she disliked having to
live away from her family for the months spent in Canada. She also
wanted to pursue a career in film."

Highlander Worldwide: The Buzz
http://www.highlanderworldwide.com/newsletter/buzz/buzz01.pdf

"Vandernoot, homesick for Paris (where the series filmed half its
episodes, due to a co-production deal), chose to leave the series at
the start of the second season."

Sitcoms Online: Highlander
http://www.sitcomsonline.com/photopost/showphoto.php/photo/23764/sort/2/cat/500

"After the conclusion of the first season, Vandernoot decided to leave
HIGHLANDER to pursue a feature film career back home in Paris. And so
the producers where forced to create the dramatic end to her character
in the episode, 'The Darkness,' during the second season. More
recently, Vandernoot has appeared in a made-for-TV movie and started a
family in Paris."

SF Site: Highlander: The Series
http://www.sfsite.com/depts/hlpromo02.htm

"Early in the second season, Alexandra Vandernoot told the producers
she didn't want to be on the show anymore - which lead the writers to
kill her off."

Amazon: Quotes & Trivia: Highlander The Series
http://www.amazon.com/exec/obidos/tg/detail/-/B0001BKBGQ/104-8867107-6979939?v=glance&vi=quotes-trivia

My Google search strategy:

Google Web Search: vandernoot tessa highlander "written out" OR "to leave"
://www.google.com/search?hl=en&q=vandernoot+tessa+highlander+%22written+out%22+OR+%22to+leave%22

I hope this is helpful. If anything is unclear or incomplete, or if a
link doesn't work for you, please request clarification; I'll gladly
offer further assistance before you rate my answer.

Best regards,
pinkfreud