Carbon dioxide and ammonia undergo ornithine cycle in the liver cells. It takes place in five major steps. The extra proteins in the body are degraded by the process of deamination where the NH2​ group is removed and it is converted into ammonium ions in the liver. 

a) The ammonium ions combines with carbon dioxide in the presence of enzyme carbomyl phosphate synthase. It consumes two molecules of ATP.

b) Carbamoyl phosphate is converted to citrulline by enzyme ornithine transcarbamoylase.

c) A condensation reaction occurs between the amino group of aspartate and the carbonyl group of citrulline to form argininosuccinate. This reaction is ATP dependent and is catalyzed by argininosuccinate synthetase.

d) Argininosuccinate undergoes cleavage by argininosuccinase to form arginine and fumarate.

e) Arginine is cleaved by arginase to form urea and ornithine.

As urea is a nitrogen containing By product of metabolism, it's breakdown occurs in liver in the presence of Urease enzyme. But the enzyme or enzymes involved in urea formation in the first place must be a bit complex, a multi step process maybe. Also to add to your question, does urea formation take place in the whole body (waste product) or only in liver. Breakdown does happen in liver though. Maybe the next one will answer.(Sorry Anushka, to add up to your confusion. Nice question)