when your lawyer relinquish himself does the court give you more time to find a new lawyer

I assume you mean that the lawyer withdrew. If so, unless you fired the lawyer at the last minute, the court will usually allow additional time to find a new attorney. In my experience it is rare for a court to require someone to dispose of their case without representation. There are exceptions, usually when there have been many other attorneys and the person requesting representation is at fault for the lack of representation.