Please add completion for latexmk. I think that it should at least
behave like "latex".

Supporting options too (listed by "latexmk -h") would be fine.

Do you mean complete *.(tex|TEX|texinfo|texi)(-.) ?
For the record, these are

Usage: latexmk [latexmk_options] [filename ...]

  Latexmk_options:
   -bm <message> - Print message across the page when converting to postscript
   -bi <intensity> - Set contrast or intensity of banner
   -bs <scale> - Set scale for banner
   -commands  - list commands used by latexmk for processing files
   -c     - clean up (remove) all nonessential files, except
            dvi, ps and pdf files
   -C     - clean up (remove) all nonessential files
            including aux, dep, dvi, postscript and pdf files
   -c1    - clean up (remove) all nonessential files,
            including dvi, pdf and ps files, but excluding aux and dep files
   -d     - Print `DRAFT' across the page when converting to postscript
   -dF <filter> - Filter to apply to dvi file
   -dvi   - generate dvi
   -dvi-  - turn off required dvi
   -f     - force continued processing past errors
   -f-    - turn off forced continuing processing past errors
   -F     - Ignore non-existent files when making dependencies
   -F-    - Turn off -F
   -g     - process regardless of file timestamps
   -g-    - Turn off -g
   -h     - print help
   -help - print help
   -i     - rescan for input if dependency file older than tex file
   -i-    - Turn off -i
   -il    - make list of input files by parsing log file
   -it    - make list of input files by parsing tex file
   -I     - force rescan for input files
   -I-    - Turn off -I
   -l     - force landscape mode
   -l-    - turn off -l
   -pdf   - generate pdf by pdflatex
   -pdfdvi - generate pdf by dvipdf
   -pdfps - generate pdf by ps2pdf
   -pdf-  - turn off pdf
   -ps    - generate postscript
   -ps-   - turn off postscript
   -pF <filter> - Filter to apply to postscript file
   -p     - print document after generating postscript.
            (Can also print .dvi or .pdf files -- see documentation)
   -print=dvi - print dvi file
   -print=ps  - print ps file
   -print=pdf - print pdf file
   -pv    - preview document.  (Side effect turn off continuous preview)
   -pv-   - turn off preview mode
   -pvc   - preview document and continuously update.  (This also turns
                on force mode, so errors do not cause latexmk to stop.)
            (Side effect: turn off ordinary preview mode.)
   -pvc-  - turn off -pvc
   -r <file> - Read custom RC file
   -silent  - silence progress messages from called programs
   -v     - display program version
   -verbose - display usual progress messages from called programs
   -version      - display program version
   -view=default - viewer is default (dvi, ps, pdf)
   -view=dvi     - viewer is for dvi
   -view=ps      - viewer is for ps
   -view=pdf     - viewer is for pdf
   filename = the root filename of LaTeX document

At least .tex and .TEX, probably not .texinfo and .texi, but I wonder
why these extensions are selected for latex.

out and add all the latexmk options.

Index: Completion/Unix/Type/_tex
===================================================================
RCS file: /cvsroot/zsh/zsh/Completion/Unix/Type/_tex,v
retrieving revision 1.5
diff -u -r1.5 _tex
--- Completion/Unix/Type/_tex	26 Sep 2007 05:21:49 -0000	1.5
+++ Completion/Unix/Type/_tex	11 Jul 2009 01:47:48 -0000
@@ -1,4 +1,4 @@
-#compdef tex latex slitex pdflatex jadetex pdfjadetex xetex=tex xelatex=latex
+#compdef tex latex slitex pdflatex jadetex pdfjadetex xetex=tex xelatex=latex latexmk

 local expl