What I tend to do is write a conditional (or do do it by hand if it's a static HTML site) so that on the home page it says:
<a href="http://mysite.com">My site</a>
but on all other pages it says:
<a href="http://mysite.com" rel="nofollow">My site</a>
That way you get the benefit of the link juice from the home page (which is usually the strongest page) which isn't then eroded by having a site-wide link.
Alternatively you could make the link live on the home page only, and on all other pages have it writen in static text:
<p>Site by me</p> without a link.
As for the
rel="designer", I haven't come across that before.