Partition in joint property

As the other two brothers can execute a relinquishment deed for their respective shares in favour of 3rd brother.

Yes, that is also an option, but even after executing a relinquishment deed, it won’t be clear how much portion belongs to whom and in which specific area. That’s why I feel that going for a partition by mutual consent is the right approach.?????

By partitioning or by knowing how much is the share of each individual ,may not make any difference because the other cosharers have already decided to transfer their share in the property in favor of the chosen brother.

Therefore it is advisable that they may transfer their share in the property to the chosen brother by executing a registered gift deed, the relinquishment  deed may not be applicable for the property purchased jointly by all the three. 

Yes, partition would be the best option provided there are no conditions to the contrary in the citations sale deed.

Since both of them want to donate their respective share(s) in favour of third one, "GIFT DEED" should be registered.

Partition of the property shall not serve any purpose except to generate some work of the lawyers and court, since both brothers are willing to leave their share(s) in favour of third brother, subsequently entire property shall devolve upon the donee brother. 

Since the property is self-acquired it cannot be relinquished by the two brothers in favour of third one.

To my knowledge and understanding there is nothing that prevents the brothers partitioning the property based on their mutual understanding. They owe no explanation to any third party, public authorities included some among  them got less and others, more. In a partition, the apportionment need not based physical measurements alone. Everything, such as location, future potentials etc.etc.