Cutting the plasmid within a region of homology both targets the plasmid to the site of homology and greatly enhances the efficiency of integration.You want to use plasmids without centromeres or 2 micron origins because integrating them causes chromosome instability.  There would be an effect of the length of this homology, and perhaps an effect of the actual sequence, but the key thing is to make the double strand break in the yeast sequence on the plasmid that you are using to target the integration.

There's a special class of vectors (integrative vectors) lacking centromeric or 2 micron regions, e.g. YIplac128, YIplac204, YIplac211. Have a look here: www.snapgene.com/resources/plasmid_files/yeast_plasmids/. Several markers are available. After cloning your favorite gene into the multiple cloning site, you can linearize the plasmid in the marker gene (make sure that the restriction enzyme used only cuts once in the plasmid) and transform the yeasties with  the LiAcetat method. Usually you get a good number of transformants due to long stretches of homology.

You may also find that you get a higher efficiency if you transform into diploids (and then sporulate, or not, according to what you are going to do next). - This is also useful if the cells don't grow well with the gene knocked out.

Remember to include a 'no DNA' control, so you have a sense for what the background is.

These are some tips to increase the efficiency of transformation for plasmid integration:

-Use exponentially growing yeast cells for transformation

-After the transformation with LiAc procedure, let grow the cells for one generation to select transformants and then plate on selective solid medium