implanted, planted, rooted

Webster's Dictionary (GCIDE)

1.brought about or set up or accepted; especially long and widely accepted; as, distrust of established authority; a team established as a member of a major league; enjoyed his prestige as an established writer; an established precedent; the established Church. Contrasted with unestablished. [Narrower terms: entrenched; implanted, planted, rooted; official; recognized] [WordNet 1.5]

2.securely established; as, an established reputation.

Syn: firm. [WordNet 1.5]

3.settled securely and unconditionally.

Syn: accomplished, effected. [WordNet 1.5]

4.conforming with accepted standards. [WordNet 1.5]

5.shown to be valid beyond a reasonable doubt; as, the established facts in the case.

Syn: proved. [WordNet 1.5 +PJC]

6.(Bot.) introduced from another region and persisting without cultivation; -- of plants.

Syn: naturalized. [WordNet 1.5 +PJC]