My father has taken care of two sections of property adjoining his property. He over 40 years has kept the brush and grass cleaned up and has utilized the property as a garden for all those years, no one else has taken the responsibility to keep it clean. The largest portion of the property belongs to the heirs on my mothers side of the family. We wish to file Adverse Possession, how will the heirs affect the process and what is the obgliations on back taxes. It amounts to about 10 or so acres.

While each state has their own rules as applied to Adverse Possession they have many things in common.

The government does not make it simple or easy for anyone to steal real estate from another person.

Conditions for Alienation by Adverse Possession are:
Hostile Possession of the property, to the exclusion of the true owner or any who may contest it.
Open Possession with no attempt to conceal occupancy
Taxes paid on the property by the adverse possessor during all the years of possession.
Claim of the Title, even an imperfect one, thus creating a reasonable basis for the action. (don't confuse this with a fraudulent title... or you go to jail)
Adverse possession must to continuous for a set number of years with out the consent of the owner.
Notorious and flagrant public possession of the property.

Successful claims for Adverse Possession are very rare, almost unheard of except in Urban Legend and a claimant is far more likely to find himself the subject of a suite for Slander Of Title which would be far easier to prove simply by the attempt at Adverse Possession by the claimant.

Why not attempt a far more realistic and respectable way... see if the real owners want to sale. It would probably be far less expensive than your legal bills would be.