I just watched P Allen Smiths garden home he says it contains trace minerals and lime. I wouldnt apply it too thick. When I have a bonfire the ashes and coals go in my compost.

Depends on your soil. Especially its pH and amout of potassium. Below is a pretty good article.

Here is a link that might be useful: Haul ash?

They are extremely alkaline. It's not recommended for places with alkaline soil.

Depending on the quantity and depending on your soil you may be creating more problems than you want to deal with. Wood ash is extremely alkaline and does have large numbers of nutrients like Phosphorus and Potash and Calcium Carbonate that can disrubt the normal levels of nutrients in your soil and/or can interfere with a plants ability to uptake other, essential, nutrients. For example excess P in a soil inhibits a plants ability to uptake Zinc, Iron, and Cobalt, all micronutrients but essential for healthy growth. Excess K can inhibit a plants abiltiy to uptake necessary Nitrogne and excess Calcium inhibits the uptake of necessary Magbesium.
This is one of many reasons why testing your soil before adding this material is necessary.